On Noncommutative Integral Standard Generalized Table Algebras of Dimension 6

We will investigate the structure of noncommutative imprimitive association schemes of rank 6 and the representation of their adjacency algebras. From this investigation, we will construct new integral standard generalized table algebras with three parameters. These algebras are noncommutative, imprimitive, and 6-dimensional.     

On Homogeneous Standard Integral Table Algebras of Degree 4

In this paper we classify, up to exact isomorphism, the algebras in the title which contain a faithful element and in which every non-trivial table subset has dimension at least five.     

On Generalized CB-Degenerations of Algebras

We introduce a concept generalizing classical degenerations of algebras (defined by structure constants) and Crawley-Boevey degenerations introduced in [3 Crawley-Boevey , W. W. ( 1995 ). Tameness of biserial algebras . Arch. Math. 65 : 399 – 407 .[Crossref], [Web of Science ®] , [Google Scholar]]. We prove that if A ₀ is such a generalized degeneration of A ₁ and the algebras have equal dimensions, then A ₀ is a degeneration of A ₁ in the classical sense.     

一类广义Heisenberg-Virasoro代数的导子

主要研究了一类非有限分次的广义Heisenberg-Virasoro代数HV,并给出了HV导子的具体结构.为了计算HV的导子Der HV,可以把它分解成内导子adHV和阶为零次的导子(Der HV)_0之和.     

量子广义Kac-Moody代数的整形式

主要讨论一阶量子广义Kac-Moody代数U_q(2α)的结构,其中a∈Z0.在此基础上,刻画了量子广义代数U_q(g)的另一种整形式.     

标准算子代数上满足某些等式的广义导子的刻画(英文)

令H为复数域C上的Hilbert空间,A为H上的标准算子代数.设δ:A→B(H)是线性映射.本文证明了,如果对任意A∈A成立δ(AA~*A)=δ(A)A~*A-Aδ(A~*)A+AA~*δ(A),则存在λ∈C及算子S,T∈B(H)满足S+T=λI,使得对所有的A∈A都有δ(A)=SA-AT.     

Embedding of Lie Algebras in Isogeneralized Structurable Algebras

In a previous paper, the first-named author introduced generalized structurable algebras, while the second-named author introduced the isotopies of Lie algebras. In this paper, we combine the two analyses, submit the notion of isogeneralized structural algebras, and show that they include Lie algebras, all their axiom-preserving generalizations of graded, supersymmetric or isotopic type, as well as numerous other algebras.     

二元广义外代数的Hochschild同调群

设Aq=k／(x2,xy+qyx,y2)是含有两个变量的广义外代数,基于Buch- weitz等人构造的极小投射双模解,广义外代数的各阶Hochschild同调群的维数被清晰地计算．     

Commutative Standard Table Algebras with at Most One Nontrivial Multiplicity

We classify commutative standard table algebras (STA) with at most one nontrivial multiplicity. The main result shows that there exists exactly one nontrivial multiplicity if and only if the table basis is the wreath product of a two-dimensional subalgebra and an abelian group. The theorem applies to adjacency algebras of commutative association schemes with exactly one primitive idempotent matrix of rank greater than one. A theorem of Seitz that characterizes finite groups with exactly one irreducible representation of degree greater than one is another corollary of the main theorem.     

On Homogeneous Weighted Algebras

We extend the concept of the “join” to the case of infinitely many weighted algebras. We study the problem of its uniqueness (up to weighted isomorphism) which gives rise to a natural notion of homogeneous weighted algebras. We show that several classes of weighted algebras coming from genetics are homogeneous and that homogeneity is preserved by duplication. Finally, we examine some well-known weighted algebras satisfying identities, as Bernstein, train, and evolution algebras.     

Structures of Not-finitely Graded Lie Algebras Related to Generalized Virasoro Algebras

In this paper, we study the structure theory of a class of not-finitely graded Lie algebras related to generalized Virasoro algebras. In particular, the derivation algebras, the automorphism groups and the second cohomology groups of these Lie algebras are determined.     

Generalized Group Algebras of Locally Compact Groups

This article studies the homological properties of generalized group algebra L ¹(G, A) of a locally compact group G over a Banach algebra A with an identity of norm 1. It is shown that if L ¹(G, A) is right continuous then G is finite and A is right continuous. It is also shown that L ¹(G, A) is right self-injective if and only if G is finite and A is right self-injective.     

Finite-dimensional Representations for a Class of Generalized Intersection Matrix Lie Algebras

In this paper, the authors study a class of generalized intersection matrix Lie algebras gim(M_n), and prove that its every finite-dimensional semisimple quotient is of type M(n, a, c, d). Particularly, any finite dimensional irreducible gim(M_n) module must be an irreducible module of Lie algebra of type M(n, a, c, d) and any finite dimensional irreducible module of Lie algebra of type M(n, a, c, d) must be an irreducible module of gim(M_n).     

算子代数的斜积

引入了算子代数的一种新运算"斜积",证明了在这个新定义的斜积运算下算子代数的自反性保持不变.研究发现,斜积运算对应的子空间格是拓扑意义下的格的直积关系.这个新发现的重要意义在于由此可从已知的自反子空间格生成更多更复杂的新自反格,从而得到新的自反代数.在此基础上,本文对KS-代数保持性等其他非自伴代数类的性质也作了相应研究.     

广义路代数与点Hopf代数

Most of pointed Hopf algebras of dimension p^m with large coradtical are shown to be generalized path algebras. By the theory of generalized path algebras, the representations, homological dimensions and radicals of these Hopf algebras are obtained. The relations between the radicals of path algebras and connectivity of directed graphs are given.     

On Bernstein Algebras Satisfying Chain Conditions

Our aim in this article is to study Noetherian and Artinian Bernstein algebras. We show that for Bernstein algebras which are either Jordan or nuclear, each of the Noetherian and Artinian conditions implies finite dimensionality. This result fails for general Noetherian or Artinian Bernstein algebras. We also investigate the relationships between the three finiteness conditions: Noetherian, Artinian, and finitely generated. Especially, we prove that Noetherian Bernstein algebras are finitely generated.     

New Results on Generalized $c$-Distance Without Continuity in Cone $b$-Metric Spaces over Banach Algebras

In this work, some new fixed point results for generalized Lipschitz mappings on generalized $c$-distance in cone $b$-metric spaces over Banach algebras are obtained, not acquiring the condition that the underlying cone should be normal or the mappings should be continuous. Furthermore, the existence and the uniqueness of the fixed point are proven for such mappings. These results greatly improve and generalize several well-known comparable results in the literature. Moreover, some examples and an application are given to support our new results.