We provide an equivalence between the dg category of coherent matrix factorizations and a certain dg category of absolute singularities. As an application, we compute the l-adic cohomology of the dg category of coherent matrix factorizations, as well as its Hochschild and periodic cyclic homologies (these last two only in the affine case).
{"title":"On some (co)homological invariants of coherent matrix factorizations","authors":"Massimo Pippi","doi":"10.4171/jncg/515","DOIUrl":"https://doi.org/10.4171/jncg/515","url":null,"abstract":"We provide an equivalence between the dg category of coherent matrix factorizations and a certain dg category of absolute singularities. As an application, we compute the l-adic cohomology of the dg category of coherent matrix factorizations, as well as its Hochschild and periodic cyclic homologies (these last two only in the affine case).","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45364044","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}
We study the geometry in the perturbations of principal submodules in the Drury-Arveson space. We show that the perturbations give rise to smooth vector bundles of Hilbert spaces which are equipped with natural Hermitian connections. We compute the associated parallel transport operators and explore properties of the monodromy.
{"title":"Perturbations of principal submodules in the Drury–Arveson space","authors":"M. Jabbari, Xiang Tang","doi":"10.4171/jncg/469","DOIUrl":"https://doi.org/10.4171/jncg/469","url":null,"abstract":"We study the geometry in the perturbations of principal submodules in the Drury-Arveson space. We show that the perturbations give rise to smooth vector bundles of Hilbert spaces which are equipped with natural Hermitian connections. We compute the associated parallel transport operators and explore properties of the monodromy.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48341703","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}
We define the Chern character of the index class of a $G$-invariant family of $G$-transversally elliptic operators, see [6]. Next we study the Berline–Vergne formula for families in the elliptic and transversally elliptic case.
{"title":"The index of $G$-transversally elliptic families. II","authors":"Alexandre Baldare","doi":"10.4171/jncg/390","DOIUrl":"https://doi.org/10.4171/jncg/390","url":null,"abstract":"We define the Chern character of the index class of a $G$-invariant family of $G$-transversally elliptic operators, see [6]. Next we study the Berline–Vergne formula for families in the elliptic and transversally elliptic case.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":"67 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138524481","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}
{"title":"Symmetries of slice monogenic functions","authors":"F. Colombo, R. S. Kraußhar, I. Sabadini","doi":"10.4171/jncg/387","DOIUrl":"https://doi.org/10.4171/jncg/387","url":null,"abstract":"","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":"14 1","pages":"1075-1106"},"PeriodicalIF":0.9,"publicationDate":"2020-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44123228","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}
We prove a Runge theorem for and describe the homology of axially symmetric open subsets of H.
我们证明了一个Runge定理，并描述了H的轴对称开子集的同调性。
{"title":"On Runge pairs and topology of axially symmetric domains","authors":"C. Bisi, J. Winkelmann","doi":"10.4171/JNCG/409","DOIUrl":"https://doi.org/10.4171/JNCG/409","url":null,"abstract":"We prove a Runge theorem for and describe the homology of axially symmetric open subsets of H.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48399061","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}
In this note, we give a short proof of the localization formula for the loop space Chern character of a compact Riemannian spin manifold M, using the rescaled spinor bundle on the tangent groupoid associated to M.
在本文中，我们给出了紧黎曼自旋流形M的环空间Chern特征的局部化公式的一个简短证明。
{"title":"A short proof of the localization formula for the loop space Chern character of spin manifolds","authors":"Matthias Ludewig, Zelin Yi","doi":"10.4171/jncg/464","DOIUrl":"https://doi.org/10.4171/jncg/464","url":null,"abstract":"In this note, we give a short proof of the localization formula for the loop space Chern character of a compact Riemannian spin manifold M, using the rescaled spinor bundle on the tangent groupoid associated to M.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46307521","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}
{"title":"On anchored Lie algebras and the Connes–Moscovici bialgebroid construction","authors":"P. Saracco","doi":"10.4171/JNCG/475","DOIUrl":"https://doi.org/10.4171/JNCG/475","url":null,"abstract":"We show how the Connes-Moscovici's bialgebroid construction naturally provides universal objects for Lie algebras acting on non-commutative algebras.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49515172","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}
Let $G$ be a linear Lie group acting properly and isometrically on a $G$-spin$^c$ manifold $M$ with compact quotient. We show that Poincare duality holds between $G$-equivariant $K$-theory of $M$, defined using finite-dimensional $G$-vector bundles, and $G$-equivariant $K$-homology of $M$, defined through the geometric model of Baum and Douglas.
{"title":"An equivariant Poincaré duality for proper cocompact actions by matrix groups","authors":"Haoyang Guo, V. Mathai","doi":"10.4171/jncg/468","DOIUrl":"https://doi.org/10.4171/jncg/468","url":null,"abstract":"Let $G$ be a linear Lie group acting properly and isometrically on a $G$-spin$^c$ manifold $M$ with compact quotient. We show that Poincare duality holds between $G$-equivariant $K$-theory of $M$, defined using finite-dimensional $G$-vector bundles, and $G$-equivariant $K$-homology of $M$, defined through the geometric model of Baum and Douglas.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45594666","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}
We characterize the lifting property (LP) of a separable $C^*$-algebra $A$ by a property of its maximal tensor product with other $C^*$-algebras, namely we prove that $A$ has the LP if and only if for any family $({D_imid iin I}$ of $C^*$-algebras the canonical map $$ {ell_infty({D_i}) otimes_{max} A}to {ell_infty({D_i otimes_{max} A}) }$$ is isometric. Equivalently, this holds if and only if $M otimes_{max} A= M otimes_{rm nor} A$ for any von Neumann algebra $M$.
{"title":"On the lifting property for $C^*$-algebras","authors":"G. Pisier","doi":"10.4171/jncg/473","DOIUrl":"https://doi.org/10.4171/jncg/473","url":null,"abstract":"We characterize the lifting property (LP) of a separable $C^*$-algebra $A$ by a property of its maximal tensor product with other $C^*$-algebras, namely we prove that $A$ has the LP if and only if for any family $({D_imid iin I}$ of $C^*$-algebras the canonical map $$ {ell_infty({D_i}) otimes_{max} A}to {ell_infty({D_i otimes_{max} A}) }$$ is isometric. Equivalently, this holds if and only if $M otimes_{max} A= M otimes_{rm nor} A$ for any von Neumann algebra $M$.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48950866","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}
The Arens-Michael functor in noncommutative geometry is an analogue of the analytification functor in algebraic geometry: out of the ring of "algebraic functions" on a noncommutative space it constructs the ring of "holomorphic functions" on it. In this paper, we explicitly compute the Arens-Michael envelopes of the Jordanian plane and the quantum enveloping algebra $U_q(mathfrak{sl}(2))$ of $mathfrak{sl}(2)$ for $|q|=1$.
{"title":"The Arens-Michael envelopes of the Jordan plane and $U_q(mathfrak{sl}(2))$","authors":"Dmitrii Pedchenko","doi":"10.4171/jncg/461","DOIUrl":"https://doi.org/10.4171/jncg/461","url":null,"abstract":"The Arens-Michael functor in noncommutative geometry is an analogue of the analytification functor in algebraic geometry: out of the ring of \"algebraic functions\" on a noncommutative space it constructs the ring of \"holomorphic functions\" on it. In this paper, we explicitly compute the Arens-Michael envelopes of the Jordanian plane and the quantum enveloping algebra $U_q(mathfrak{sl}(2))$ of $mathfrak{sl}(2)$ for $|q|=1$.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44687193","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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