We consider algebras with basis numerated by elements of a group G. We fix a function f from G × G to a ground field and give a multiplication of the algebra which depends on f. We study the basic properties of s...We consider algebras with basis numerated by elements of a group G. We fix a function f from G × G to a ground field and give a multiplication of the algebra which depends on f. We study the basic properties of such algebras. In particular, we find a condition on f under which the corresponding algebra is a Leibniz algebra. Moreover, for a given subgroup G of G we define a G-periodic algebra, which corresponds to a G-periodic function f, we establish a criterion for the right nilpotency of a G-periodic algebra. In addition, for （7 = Z we describe all 2Z- and 3Z-periodic algebras. Some properties of nZ-periodic algebras are obtained.展开更多
We study the relations between two groups related to cluster automorphism groups which are defined by Assem,Schiffler and Shamchenko.We establish the relation-ships among(strict)direct cluster automorphism groups and ...We study the relations between two groups related to cluster automorphism groups which are defined by Assem,Schiffler and Shamchenko.We establish the relation-ships among(strict)direct cluster automorphism groups and those groups consisting of periodicities of labeled seeds and exchange matrices,respectively,in the language of short exact sequences.As an application,we characterize automorphism-finite cluster algebras in the cases of bipartite seeds or finite mutation type.Finally,we study the relation between the group Aut(A)for a cluster algebra A and the group AutMn(S)for a mutation group Mn and a labeled mutation class S,and we give a negative answer via counter-examples to King and Pressland's problem.展开更多
We construct a class of C*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[Ml1,·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C*-al...We construct a class of C*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[Ml1,·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C*-algebra C*r(Γ, σ) for the pointwise multiplication operator Mlon l2(Γ), induced by a proper length function l on Γ with the property of bounded θ-dilation. Moreover, the compact quantum metric space structures depend only on the cohomology class of 2-cocycles in the Lipschitz isometric sense.展开更多
We study finite group actions on Leibniz algebras, and define equivariant cohomology groups associated to such actions. We show that there exists a cup-product operation on this graded cohomology, which makes it a gra...We study finite group actions on Leibniz algebras, and define equivariant cohomology groups associated to such actions. We show that there exists a cup-product operation on this graded cohomology, which makes it a graded Zinbiel algebra.展开更多
We study the structure of the generalized 2-dim affine-Virasoro algebra, and describe its automorphism group. Furthermore, we also determine the irreducibility of a Verma module over the generalized 2-dim affine-Viras...We study the structure of the generalized 2-dim affine-Virasoro algebra, and describe its automorphism group. Furthermore, we also determine the irreducibility of a Verma module over the generalized 2-dim affine-Virasoro algebra.展开更多
文摘We consider algebras with basis numerated by elements of a group G. We fix a function f from G × G to a ground field and give a multiplication of the algebra which depends on f. We study the basic properties of such algebras. In particular, we find a condition on f under which the corresponding algebra is a Leibniz algebra. Moreover, for a given subgroup G of G we define a G-periodic algebra, which corresponds to a G-periodic function f, we establish a criterion for the right nilpotency of a G-periodic algebra. In addition, for （7 = Z we describe all 2Z- and 3Z-periodic algebras. Some properties of nZ-periodic algebras are obtained.
文摘We study the relations between two groups related to cluster automorphism groups which are defined by Assem,Schiffler and Shamchenko.We establish the relation-ships among(strict)direct cluster automorphism groups and those groups consisting of periodicities of labeled seeds and exchange matrices,respectively,in the language of short exact sequences.As an application,we characterize automorphism-finite cluster algebras in the cases of bipartite seeds or finite mutation type.Finally,we study the relation between the group Aut(A)for a cluster algebra A and the group AutMn(S)for a mutation group Mn and a labeled mutation class S,and we give a negative answer via counter-examples to King and Pressland's problem.
基金supported by National Natural Science Foundation of China(Grant Nos.11171109 and 11801177)the Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000)。
文摘We construct a class of C*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[Ml1,·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C*-algebra C*r(Γ, σ) for the pointwise multiplication operator Mlon l2(Γ), induced by a proper length function l on Γ with the property of bounded θ-dilation. Moreover, the compact quantum metric space structures depend only on the cohomology class of 2-cocycles in the Lipschitz isometric sense.
文摘We study finite group actions on Leibniz algebras, and define equivariant cohomology groups associated to such actions. We show that there exists a cup-product operation on this graded cohomology, which makes it a graded Zinbiel algebra.
文摘We study the structure of the generalized 2-dim affine-Virasoro algebra, and describe its automorphism group. Furthermore, we also determine the irreducibility of a Verma module over the generalized 2-dim affine-Virasoro algebra.
