Pub Date : 2020-01-07DOI: 10.1215/21562261-2022-0034
V. Turaev
We discuss natural operations on loops in a quasi-surface and show that these operations define a structure of a quasi-Lie bialgebra in the module generated by the set of free homotopy classes of non-contractible loops.
{"title":"Quasi-Lie bialgebras of loops in quasisurfaces","authors":"V. Turaev","doi":"10.1215/21562261-2022-0034","DOIUrl":"https://doi.org/10.1215/21562261-2022-0034","url":null,"abstract":"We discuss natural operations on loops in a quasi-surface and show that these operations define a structure of a quasi-Lie bialgebra in the module generated by the set of free homotopy classes of non-contractible loops.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48031619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-31DOI: 10.1215/21562261-2022-0017
K. Neeb
Let V be a standard subspace in the complex Hilbert space H and U : G to U(H) be a unitary representation of a finite dimensional Lie group. We assume the existence of an element h in the Lie algebra of G such that U(exp th) is the modular group of V and that the modular involution J_V normalizes U(G). We want to determine the semigroup $S_V = { gin G : U(g)V subseteq V}.$ In previous work we have seen that its infinitesimal generators span a Lie algebra on which ad h defines a 3-grading, and here we completely determine the semigroup S_V under the assumption that ad h defines a 3-grading. Concretely, we show that the ad h-eigenspaces for the eigenvalue $pm 1$ contain closed convex cones $C_pm$, such that $S_V = exp(C_+) G_V exp(C_-)$, where $G_V$ is the stabilizer of V in G. To obtain this result we compare several subsemigroups of G specified by the grading and the positive cone $C_U$ of U. In particular, we show that the orbit U(G)V, endowed with the inclusion order, is an ordered symmetric space covering the adjoint orbit $Ad(G)h$, endowed with the partial order defined by~$C_U$.
{"title":"Semigroups in 3-graded Lie groups and endomorphisms of standard subspaces","authors":"K. Neeb","doi":"10.1215/21562261-2022-0017","DOIUrl":"https://doi.org/10.1215/21562261-2022-0017","url":null,"abstract":"Let V be a standard subspace in the complex Hilbert space H and U : G to U(H) be a unitary representation of a finite dimensional Lie group. We assume the existence of an element h in the Lie algebra of G such that U(exp th) is the modular group of V and that the modular involution J_V normalizes U(G). We want to determine the semigroup $S_V = { gin G : U(g)V subseteq V}.$ In previous work we have seen that its infinitesimal generators span a Lie algebra on which ad h defines a 3-grading, and here we completely determine the semigroup S_V under the assumption that ad h defines a 3-grading. Concretely, we show that the ad h-eigenspaces for the eigenvalue $pm 1$ contain closed convex cones $C_pm$, such that $S_V = exp(C_+) G_V exp(C_-)$, where $G_V$ is the stabilizer of V in G. To obtain this result we compare several subsemigroups of G specified by the grading and the positive cone $C_U$ of U. In particular, we show that the orbit U(G)V, endowed with the inclusion order, is an ordered symmetric space covering the adjoint orbit $Ad(G)h$, endowed with the partial order defined by~$C_U$.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42892192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-01DOI: 10.1215/21562261-2019-0032
T. Ashikaga
{"title":"Multidimensional continued fractions for cyclic quotient singularities and Dedekind sums","authors":"T. Ashikaga","doi":"10.1215/21562261-2019-0032","DOIUrl":"https://doi.org/10.1215/21562261-2019-0032","url":null,"abstract":"","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":"59 1","pages":"993-1039"},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45412965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-01DOI: 10.1215/21562261-2019-0027
Haian He, Toshihisa Kubo, R. Zierau
{"title":"On the reducibility of scalar generalized Verma modules associated to maximal parabolic subalgebras","authors":"Haian He, Toshihisa Kubo, R. Zierau","doi":"10.1215/21562261-2019-0027","DOIUrl":"https://doi.org/10.1215/21562261-2019-0027","url":null,"abstract":"","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":"59 1","pages":"787-813"},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47302573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-11DOI: 10.1215/21562261-2021-0002
Yunhyung Cho, Yoosik Kim, Y. Oh
Using the bulk-deformation of Floer cohomology by Schubert cycles and non-Archimedean analysis of Fukaya--Oh--Ohta--Ono's bulk-deformed potential function, we prove that every complete flag manifold $mathrm{Fl}(n)$ ($n geq 3$) with a monotone Kirillov--Kostant--Souriau symplectic form carries a continuum of non-displaceable Lagrangian tori which degenerates to a non-torus fiber in the Hausdorff limit. In particular, the Lagrangian $S^3$-fiber in $mathrm{Fl}(3)$ is non-displaceable, answering the question of which was raised by Nohara--Ueda who computed its Floer cohomology to be vanishing.
{"title":"A critical point analysis of Landau–Ginzburg potentials with bulk in Gelfand–Cetlin systems","authors":"Yunhyung Cho, Yoosik Kim, Y. Oh","doi":"10.1215/21562261-2021-0002","DOIUrl":"https://doi.org/10.1215/21562261-2021-0002","url":null,"abstract":"Using the bulk-deformation of Floer cohomology by Schubert cycles and non-Archimedean analysis of Fukaya--Oh--Ohta--Ono's bulk-deformed potential function, we prove that every complete flag manifold $mathrm{Fl}(n)$ ($n geq 3$) with a monotone Kirillov--Kostant--Souriau symplectic form carries a continuum of non-displaceable Lagrangian tori which degenerates to a non-torus fiber in the Hausdorff limit. In particular, the Lagrangian $S^3$-fiber in $mathrm{Fl}(3)$ is non-displaceable, answering the question of which was raised by Nohara--Ueda who computed its Floer cohomology to be vanishing.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43157906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-24DOI: 10.1215/21562261-2022-0013
Reza Abdolmaleki, J. Herzog, G. Zhu
Let $S=K[x_1,ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$. In this paper, we compute the socle of $cb$-bounded strongly stable ideals and determine that the saturation number of strongly stable ideals and of equigenerated $cb$-bounded strongly stable ideals. We also provide explicit formulas for the saturation number $sat(I)$ of Veronese type ideals $I$. Using this formula, we show that $sat(I^k)$ is quasi-linear from the beginning and we determine the quasi-linear function explicitly.
{"title":"The saturation number of c-bounded stable monomial ideals and their powers","authors":"Reza Abdolmaleki, J. Herzog, G. Zhu","doi":"10.1215/21562261-2022-0013","DOIUrl":"https://doi.org/10.1215/21562261-2022-0013","url":null,"abstract":"Let $S=K[x_1,ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$. In this paper, we compute the socle of $cb$-bounded strongly stable ideals and determine that the saturation number of strongly stable ideals and of equigenerated $cb$-bounded strongly stable ideals. We also provide explicit formulas for the saturation number $sat(I)$ of Veronese type ideals $I$. Using this formula, we show that $sat(I^k)$ is quasi-linear from the beginning and we determine the quasi-linear function explicitly.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45726332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-03DOI: 10.1215/21562261-2019-0049
Heer Zhao
For a semi-stable abelian variety A_K over a complete discrete valuation field K, we show that every finite subgroup scheme of A_K extends to a log finite flat group scheme over the valuation ring of K endowed with the canonical log structure. To achieve this, we first prove that every weak log abelian variety over an fs log scheme with its underlying scheme locally noetherian, is a sheaf for the Kummer flat topology, which answers a question of Chikara Nakayama. We also give several equivalent conditions defining isogenies of log abelian varieties.
{"title":"Extending finite-subgroup schemes of semistable abelian varieties via log-abelian varieties","authors":"Heer Zhao","doi":"10.1215/21562261-2019-0049","DOIUrl":"https://doi.org/10.1215/21562261-2019-0049","url":null,"abstract":"For a semi-stable abelian variety A_K over a complete discrete valuation field K, we show that every finite subgroup scheme of A_K extends to a log finite flat group scheme over the valuation ring of K endowed with the canonical log structure. To achieve this, we first prove that every weak log abelian variety over an fs log scheme with its underlying scheme locally noetherian, is a sheaf for the Kummer flat topology, which answers a question of Chikara Nakayama. We also give several equivalent conditions defining isogenies of log abelian varieties.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44534910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-01DOI: 10.1215/21562261-2019-0022
Yuanyuan Bao, D. Daigle
Let A be a geometrically integral algebra over a field k. We prove that for any affine k-domain R, if there exists an extension field K of k such that R ⊆ K ⊗k A and R * K, then there exists an extension field L of k such that R ⊆ L ⊗k A and trdegk(L) < trdegk(R). This generalizes a result of Freudenburg, namely, the fact that this is true for A = k.
{"title":"Small embeddings of integral domains","authors":"Yuanyuan Bao, D. Daigle","doi":"10.1215/21562261-2019-0022","DOIUrl":"https://doi.org/10.1215/21562261-2019-0022","url":null,"abstract":"Let A be a geometrically integral algebra over a field k. We prove that for any affine k-domain R, if there exists an extension field K of k such that R ⊆ K ⊗k A and R * K, then there exists an extension field L of k such that R ⊆ L ⊗k A and trdegk(L) < trdegk(R). This generalizes a result of Freudenburg, namely, the fact that this is true for A = k.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41545784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-01DOI: 10.1215/21562261-2019-0021
Shota Murakami
{"title":"Deformation equivalence classes of Inoue surfaces with b1=1 and b2=0","authors":"Shota Murakami","doi":"10.1215/21562261-2019-0021","DOIUrl":"https://doi.org/10.1215/21562261-2019-0021","url":null,"abstract":"","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47703495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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