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Clifford Deformations of Koszul Frobenius Algebras and Noncommutative Quadrics
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作者 Jiwei He Yu Ye 《Algebra Colloquium》 SCIE CSCD 2024年第1期63-82,共20页
A Clifford deformation of a Koszul Frobenius algebra E is a finite dimensional Z_(2)-graded algebra E(θ),which corresponds to a noncommutative quadric hypersurface E^(!)/(z)for some central regular element z∈E_(2)^(... A Clifford deformation of a Koszul Frobenius algebra E is a finite dimensional Z_(2)-graded algebra E(θ),which corresponds to a noncommutative quadric hypersurface E^(!)/(z)for some central regular element z∈E_(2)^(!).It turns out that the bounded derived category D^(b)(gr_(Z_(2))E(θ))is equivalent to the stable category of the maximal Cohen-Macaulay modules over E^(!)/(z)provided that E!is noetherian.As a consequence,E^(!)/(z)is a noncommutative isolated singularity if and only if the corresponding Clifford deformation E(θ)is a semisimple Z_(2)-graded algebra.The preceding equivalence of triangulated categories also indicates that Clifford deformations of trivial extensions of a Koszul Frobenius algebra are related to Knörrer's periodicity theorem for quadric hypersurfaces.As an application,we recover Knörrer's periodicity theorem without using matrix factorizations. 展开更多
关键词 Koszul frobenius algebra Clifford deformation noncommutative quadric hypersurface maximal Cohen-Macaulay module
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Double Frobenius algebras 被引量:1
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作者 Zhihua WANG Libin LI 《Frontiers of Mathematics in China》 SCIE CSCD 2018年第2期399-415,共17页
Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of (strict or non-strict) double Frobenius algebras are presented. Finally, a sufficient and necessary conditi... Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of (strict or non-strict) double Frobenius algebras are presented. Finally, a sufficient and necessary condition for the trivial extension of a double Frobenius algebra to be a (strict) double Frobenius algebra is given. 展开更多
关键词 Double frobenius algebra bi-frobenius algebra trivial extension
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Measures of Asymmetry Dual to Mean Minkowski Measures of Asymmetry for Convex Bodies 被引量:2
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作者 yao dan guo qi Ji You-qing 《Communications in Mathematical Research》 CSCD 2016年第3期207-216,共10页
Khovanov type homology is a generalization of Khovanov homology.The main result of this paper is to give a recursive formula for Khovanov type homology of pretzel knots P(-n,-m, m). The computations reveal that the ... Khovanov type homology is a generalization of Khovanov homology.The main result of this paper is to give a recursive formula for Khovanov type homology of pretzel knots P(-n,-m, m). The computations reveal that the rank of the homology of pretzel knots is an invariant of n. The proof is based on a "shortcut" and two lemmas that recursively reduce the computational complexity of Khovanov type homology. 展开更多
关键词 pretzel knot Khovanov type homology frobenius algebra TQFT
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Open Frobenius Cluster-Tilted Algebras
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作者 Viviana Gubitosi 《Algebra Colloquium》 SCIE CSCD 2022年第1期1-22,共22页
In this paper,we compute the Frobenius dimension of any cluster-tilted algebra of finite type.Moreover,we give conditions on the bound quiver of a cluster-tilted algebra A such that八has non-trivial open Frobenius str... In this paper,we compute the Frobenius dimension of any cluster-tilted algebra of finite type.Moreover,we give conditions on the bound quiver of a cluster-tilted algebra A such that八has non-trivial open Frobenius structures. 展开更多
关键词 cluster-tilted algebras gentle algebras open frobenius algebras nearly Probe-nius algebras 1
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Universal Deformation Rings of Modules over Self-injective Cluster-Tilted Algebras Are Trivial
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作者 I.D.M.Gaviria JoséA.Vélez-Marulanda Peng Shan 《Algebra Colloquium》 SCIE CSCD 2021年第2期269-280,共12页
Let k be a fixed algebraically closed field of arbitrary characteristic,let Λ be a finite dimensional self-injective k-algebra,and let ∨ be an indecomposable non-projective left Λ-module with finite dimension over ... Let k be a fixed algebraically closed field of arbitrary characteristic,let Λ be a finite dimensional self-injective k-algebra,and let ∨ be an indecomposable non-projective left Λ-module with finite dimension over k.We prove that if τΛ∨ is the Auslander-Reiten translation of ∨,then the versal deformation rings R(Λ,∨)and R(Λ,τΛ∨)(in the sense of F.M.Bleher and the second author)are isomorphic.We use this to prove that if Λ is further a cluster-tilted k-algebra,then R(Λ,∨)is universal and isomorphic to k. 展开更多
关键词 self-injective cluster tilted algebras frobenius algebras (uni)versal deformation rings
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Modular derivations for extensions of Poisson algebras 被引量:3
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作者 Shengqiang WANG 《Frontiers of Mathematics in China》 SCIE CSCD 2017年第1期209-218,共10页
We compute explicitly the modular derivations for Poisson-Ore extensions and tensor products of Poisson algebras.
关键词 Poisson algebra frobenius Poisson algebra modular derivation tensor Poisson algebra
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Grbner-Shirshov Basis for Degenerate Ringel-Hall Algebras of Type F_4
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作者 Zhenzhen GAO Abdukadir OBUL 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2016年第2期199-210,共12页
In this paper, by using the Frobenius morphism and the multiplication formulas of the generic extension monoid algebra, the authors first give a presentation of the degenerate Ringel-Hall algebra, and then construct t... In this paper, by using the Frobenius morphism and the multiplication formulas of the generic extension monoid algebra, the authors first give a presentation of the degenerate Ringel-Hall algebra, and then construct the Gr¨obner-Shirshov basis for degenerate Ringel-Hall algebras of type F_4. 展开更多
关键词 Grbner-Shirshov basis frobenius map Degenerate Ringel-Hall algebras Multiplication formulas
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Quaternion rings and octonion rings
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作者 Gangyong LEE Kiyoichi OSHIRO 《Frontiers of Mathematics in China》 SCIE CSCD 2017年第1期143-155,共13页
In this paper, for rings R, we introduce complex rings C(R), quaternion rings H(R), and octonion rings O(R), which are extension rings of R; R C(R) H(R) O(R). Our main purpose of this paper is to sho... In this paper, for rings R, we introduce complex rings C(R), quaternion rings H(R), and octonion rings O(R), which are extension rings of R; R C(R) H(R) O(R). Our main purpose of this paper is to show that if R is a Frobenius algebra, then these extension rings are Frobenius Mgebras and if R is a quasi-Frobenius ring, then C(R) and H(R) are quasi-Frobenius rings and, when Char(R)=2, O(R) is also a quasi-Frobenius ring. 展开更多
关键词 Hamilton quaternion numbers Cayley-Grave's tables complex rings quaternion rings octonion rings frobenius algebras QF-rings
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