Pub Date : 2024-05-10DOI: 10.1142/s0219199724500214
Dong Liu, Yufeng Pei, Limeng Xia, Kaiming Zhao
In this paper, we present a determinant formula for a contravariant form on Verma modules over the Bondi–Metzner–Sachs (BMS) superalgebra. This formula establishes a necessary and sufficient condition for the irreducibility of the Verma modules. We then introduce and characterize a class of simple smooth modules that generalize both Verma and Whittaker modules over the BMS superalgebra. We also utilize the Heisenberg–Clifford vertex superalgebra to construct a free field realization for the BMS superalgebra. This free field realization allows us to obtain a family of natural smooth modules over the BMS superalgebra, which includes Fock modules and certain Whittaker modules.
{"title":"Smooth modules over the N = 1 Bondi–Metzner–Sachs superalgebra","authors":"Dong Liu, Yufeng Pei, Limeng Xia, Kaiming Zhao","doi":"10.1142/s0219199724500214","DOIUrl":"https://doi.org/10.1142/s0219199724500214","url":null,"abstract":"<p>In this paper, we present a determinant formula for a contravariant form on Verma modules over the <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"italic\"><mi>N</mi></mstyle><mo>=</mo><mn>1</mn></math></span><span></span> Bondi–Metzner–Sachs (BMS) superalgebra. This formula establishes a necessary and sufficient condition for the irreducibility of the Verma modules. We then introduce and characterize a class of simple smooth modules that generalize both Verma and Whittaker modules over the <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"italic\"><mi>N</mi></mstyle><mo>=</mo><mn>1</mn></math></span><span></span> BMS superalgebra. We also utilize the Heisenberg–Clifford vertex superalgebra to construct a free field realization for the <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"italic\"><mi>N</mi></mstyle><mo>=</mo><mn>1</mn></math></span><span></span> BMS superalgebra. This free field realization allows us to obtain a family of natural smooth modules over the <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"italic\"><mi>N</mi></mstyle><mo>=</mo><mn>1</mn></math></span><span></span> BMS superalgebra, which includes Fock modules and certain Whittaker modules.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-10DOI: 10.1142/s0219199724500238
Yaozhong Qiu
{"title":"A bakry-emery criterion for weighted contractivity and L2-hardy inequalities","authors":"Yaozhong Qiu","doi":"10.1142/s0219199724500238","DOIUrl":"https://doi.org/10.1142/s0219199724500238","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140991078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-07DOI: 10.1142/s0219199724500147
Brian Weber
This paper shows how a Levi-flat or pseudoconvex submanifold in a Kähler 4-manifold restricts the ambient manifold’s topology and its geometry at infinity.
本文展示了凯勒 4manifold 中的 Levi 平面或伪凸子流形如何限制环境流形的拓扑学及其在无限远处的几何形状。
{"title":"Pseudoconvex submanifolds in Kähler 4-manifolds","authors":"Brian Weber","doi":"10.1142/s0219199724500147","DOIUrl":"https://doi.org/10.1142/s0219199724500147","url":null,"abstract":"<p>This paper shows how a Levi-flat or pseudoconvex submanifold in a Kähler 4-manifold restricts the ambient manifold’s topology and its geometry at infinity.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-07DOI: 10.1142/s0219199724500184
Matthias Ostermann
In this paper, we show that any Sobolev norm of nonnegative integer order of radially symmetric functions is equivalent to a weighted Sobolev norm of their radial profile. This establishes in terms of weighted Sobolev spaces on an interval a complete characterization of radial Sobolev spaces, which was open until now. As an application, we give a description of Sobolev norms of corotational maps.
{"title":"A characterization of the subspace of radially symmetric functions in Sobolev spaces","authors":"Matthias Ostermann","doi":"10.1142/s0219199724500184","DOIUrl":"https://doi.org/10.1142/s0219199724500184","url":null,"abstract":"<p>In this paper, we show that any Sobolev norm of nonnegative integer order of radially symmetric functions is equivalent to a weighted Sobolev norm of their radial profile. This establishes in terms of weighted Sobolev spaces on an interval a complete characterization of radial Sobolev spaces, which was open until now. As an application, we give a description of Sobolev norms of corotational maps.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-04DOI: 10.1142/s0219199724500159
Claudio Gorodski, Iryna Kashuba, María Eugenia Martin
We study the variety of complex -dimensional Jordan algebras using techniques from Geometric Invariant Theory. More specifically, we use the Kirwan–Ness theorem to construct a Morse-type stratification of the variety of Jordan algebras into finitely many invariant locally closed subsets, with respect to the energy functional associated to the canonical moment map. In particular we obtain a new, cohomology-free proof of the well-known rigidity of semisimple Jordan algebras in the context of the variety of Jordan algebras.
我们利用几何不变论的技术研究了复杂 n 维乔丹代数的种类。更具体地说，我们利用基尔万-内斯（Kirwan-Ness）定理，就与经典矩映射相关的能量函数而言，将乔丹数的种类构造成有限多个不变局部封闭子集的莫尔斯型分层。特别是，我们在乔丹代数的背景下，获得了半简单乔丹代数众所周知的刚性的无同调新证明。
{"title":"A moment map for the variety of Jordan algebras","authors":"Claudio Gorodski, Iryna Kashuba, María Eugenia Martin","doi":"10.1142/s0219199724500159","DOIUrl":"https://doi.org/10.1142/s0219199724500159","url":null,"abstract":"<p>We study the variety of complex <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi></math></span><span></span>-dimensional Jordan algebras using techniques from Geometric Invariant Theory. More specifically, we use the Kirwan–Ness theorem to construct a Morse-type stratification of the variety of Jordan algebras into finitely many invariant locally closed subsets, with respect to the energy functional associated to the canonical moment map. In particular we obtain a new, cohomology-free proof of the well-known rigidity of semisimple Jordan algebras in the context of the variety of Jordan algebras.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140942339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-18DOI: 10.1142/s021919972450010x
I. Alvarez-Romero, B. Barrios, J. J. Betancor
In this paper, we consider the heat semigroup defined by the combinatorial Laplacian and two subordinated families of on homogeneous trees . We characterize the weights on for which the pointwise convergence to initial data of the above families holds for every with , where represents the counting measure in . We prove that this convergence property in is equivalent to the fact that the maximal operator on , for some , defined by the semigroup is bounded from into for some weight
{"title":"Pointwise convergence of the heat and subordinates of the heat semigroups associated with the Laplace operator on homogeneous trees and two weighted Lp maximal inequalities","authors":"I. Alvarez-Romero, B. Barrios, J. J. Betancor","doi":"10.1142/s021919972450010x","DOIUrl":"https://doi.org/10.1142/s021919972450010x","url":null,"abstract":"<p>In this paper, we consider the heat semigroup <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mo stretchy=\"false\">{</mo><msub><mrow><mi>W</mi></mrow><mrow><mi>t</mi></mrow></msub><mo stretchy=\"false\">}</mo></mrow><mrow><mi>t</mi><mo>></mo><mn>0</mn></mrow></msub></math></span><span></span> defined by the combinatorial Laplacian and two subordinated families of <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mo stretchy=\"false\">{</mo><msub><mrow><mi>W</mi></mrow><mrow><mi>t</mi></mrow></msub><mo stretchy=\"false\">}</mo></mrow><mrow><mi>t</mi><mo>></mo><mn>0</mn></mrow></msub></math></span><span></span> on homogeneous trees <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span>. We characterize the weights <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>u</mi></math></span><span></span> on <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span> for which the pointwise convergence to initial data of the above families holds for every <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo stretchy=\"false\">(</mo><mi>X</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>u</mi><mo stretchy=\"false\">)</mo></math></span><span></span> with <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mn>1</mn><mo>≤</mo><mi>p</mi><mo><</mo><mi>∞</mi></math></span><span></span>, where <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mi>μ</mi></math></span><span></span> represents the counting measure in <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span>. We prove that this convergence property in <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span> is equivalent to the fact that the maximal operator on <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mi>t</mi><mo>∈</mo><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mi>R</mi><mo stretchy=\"false\">)</mo></math></span><span></span>, for some <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><mi>R</mi><mo>></mo><mn>0</mn></math></span><span></span>, defined by the semigroup is bounded from <span><math altimg=\"eq-00014.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo stretchy=\"false\">(</mo><mi>X</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>u</mi><mo stretchy=\"false\">)</mo></math></span><span></span> into <span><math altimg=\"eq-00015.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo stretchy=\"false\">(</mo><mi>X</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>v</mi><mo stretchy=\"false\">)</mo></math></span><span></span> for some weight <span><math altimg=\"eq-00016.g","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140626157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-13DOI: 10.1142/s021919972450007x
Lucia Bagnoli, Slaven Kožić
We study the double Yangian associated with the Lie superalgebra . Our main focus is on establishing the Poincaré–Birkhoff–Witt Theorem for the double Yangian and constructing its central elements in the form of coefficients of the quantum contraction. Next, as an application, we introduce reflection algebras, certain left coideal subalgebras of the level 0 double Yangian, and find their presentations by generators and relations.
{"title":"Double Yangian and reflection algebras of the Lie superalgebra 𝔤𝔩m|n","authors":"Lucia Bagnoli, Slaven Kožić","doi":"10.1142/s021919972450007x","DOIUrl":"https://doi.org/10.1142/s021919972450007x","url":null,"abstract":"<p>We study the double Yangian associated with the Lie superalgebra <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>𝔤</mi><mi>𝔩</mi></mrow><mrow><mi>m</mi><mo>|</mo><mi>n</mi></mrow></msub></math></span><span></span>. Our main focus is on establishing the Poincaré–Birkhoff–Witt Theorem for the double Yangian and constructing its central elements in the form of coefficients of the quantum contraction. Next, as an application, we introduce reflection algebras, certain left coideal subalgebras of the level 0 double Yangian, and find their presentations by generators and relations.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-13DOI: 10.1142/s0219199724500068
Xiangsheng Wang
For the moduli space of the punctured spheres, we find a new equality between two symplectic forms defined on it. Namely, by treating the elements of this moduli space as the singular Euclidean metrics on a sphere, we give an interpretation of the complex hyperbolic form, i.e. the Kähler form of the complex hyperbolic structure on the moduli space, as a kind of Weil–Petersson form.
{"title":"The complex hyperbolic form as a Weil–Petersson form","authors":"Xiangsheng Wang","doi":"10.1142/s0219199724500068","DOIUrl":"https://doi.org/10.1142/s0219199724500068","url":null,"abstract":"<p>For the moduli space of the punctured spheres, we find a new equality between two symplectic forms defined on it. Namely, by treating the elements of this moduli space as the singular Euclidean metrics on a sphere, we give an interpretation of the complex hyperbolic form, i.e. the Kähler form of the complex hyperbolic structure on the moduli space, as a kind of Weil–Petersson form.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-10DOI: 10.1142/s0219199724500081
Shangkun Weng, Zihao Zhang
This paper concerns the structural stability of subsonic flows with a contact discontinuity in a finitely long axisymmetric cylinder. We establish the existence and uniqueness of axisymmetric subsonic flows with a contact discontinuity by prescribing the horizontal mass flux distribution, the swirl velocity, the entropy and the Bernoulli’s quantity at the entrance and the radial velocity at the exit. It can be formulated as a free boundary problem with the contact discontinuity to be determined simultaneously with the flows. Compared with the two-dimensional case, a new difficulty arises due to the singularity near the axis. An invertible modified Lagrangian transformation is introduced to overcome this difficulty and straighten the contact discontinuity. The key elements in our analysis are to utilize the deformation-curl decomposition introduced in [S. Weng and Z. Xin, A deformation-curl decomposition for three dimensional steady Euler equations, Sci. Sin. Math.49 (2019) 307–320 (in Chinese): doi:10.1360/N012018-00125] to effectively decouple the hyperbolic and elliptic modes in the steady axisymmetric Euler system and to use the implicit function theorem to locate the contact discontinuity.
本文涉及有限长轴对称圆柱体中带有接触不连续面的亚音速流动的结构稳定性。我们通过预设水平质量通量分布、漩涡速度、熵以及入口处的伯努利量和出口处的径向速度，建立了带有接触不连续面的轴对称亚音速流动的存在性和唯一性。它可以表述为一个自由边界问题，接触不连续面与流动同时确定。与二维情况相比，由于轴线附近的奇异性，出现了一个新的难题。我们引入了一种可逆的修正拉格朗日变换来克服这一困难，并使接触非连续性变直。我们分析的关键要素是利用 [S. Weng and Z. Xin, A. Lagrangian transforms, A. Lagrangian transforms, A. Lagrangian transforms, A. Lagrangian transforms, A.Weng and Z. Xin, A deformation-curl decomposition for three dimensional steady Euler equations, Sci.Math.49 (2019) 307-320 (in Chinese): doi:10.1360/N012018-00125] 中介绍的变形-卷线分解来有效地解耦稳定轴对称欧拉系统中的双曲模和椭圆模，并利用隐函数定理来定位接触间断点。
{"title":"Subsonic flows with a contact discontinuity in a finitely long axisymmetric cylinder","authors":"Shangkun Weng, Zihao Zhang","doi":"10.1142/s0219199724500081","DOIUrl":"https://doi.org/10.1142/s0219199724500081","url":null,"abstract":"<p>This paper concerns the structural stability of subsonic flows with a contact discontinuity in a finitely long axisymmetric cylinder. We establish the existence and uniqueness of axisymmetric subsonic flows with a contact discontinuity by prescribing the horizontal mass flux distribution, the swirl velocity, the entropy and the Bernoulli’s quantity at the entrance and the radial velocity at the exit. It can be formulated as a free boundary problem with the contact discontinuity to be determined simultaneously with the flows. Compared with the two-dimensional case, a new difficulty arises due to the singularity near the axis. An invertible modified Lagrangian transformation is introduced to overcome this difficulty and straighten the contact discontinuity. The key elements in our analysis are to utilize the deformation-curl decomposition introduced in [S. Weng and Z. Xin, A deformation-curl decomposition for three dimensional steady Euler equations, <i>Sci. Sin. Math.</i><b>49</b> (2019) 307–320 (in Chinese): doi:10.1360/N012018-00125] to effectively decouple the hyperbolic and elliptic modes in the steady axisymmetric Euler system and to use the implicit function theorem to locate the contact discontinuity.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-10DOI: 10.1142/s0219199724500226
Ying Dong, Shuai Zhang
{"title":"Global weak solvability in a self-consistent chemotaxis-Navier-Stokes system involving Dirichlet boundary conditions for the signal","authors":"Ying Dong, Shuai Zhang","doi":"10.1142/s0219199724500226","DOIUrl":"https://doi.org/10.1142/s0219199724500226","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140720920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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