双模问题rad~t(-,-)与拟遗传代数

设 Ｂ是 Ｋｒｕｌｌ－ｓｃｈｍｉｄｔ范畴 Ｋ上的一个上三角双模，Ｂｒｕｓｔｌｅ和 Ｈｉｌｌｅ证明了Ｂ的矩阵范畴ｍａｔＢ的投射生成子Ｐ的自同态代数的反代数Ａ是拟遗传代数，而且代数Ａ的△－好模范畴与ｍａｔＢ等价．本文把这些结果推广到由Ｃｒａｗｌｅｙ-Ｂｏｅｖｅｙ给出的具有非零导子的双模上，并在此基础上着重讨论了遗传代数 的投射模范畴Ｐｒｏｊ上的双模ｒａｄｔ（－，－），刻画了它所对应的拟遗传代数的Ｇａｂｒｉｅｌ箭图与关系，以及它们的特征模和Ｒｉｎｇｅｌ对偶．     

△-tame拟遗传代数

设(K,M,H)是上三角双模问题,Br(u)stle和Hille证明了(K,M,H)的矩阵范畴Mat(K,M)的投射生成子P的自同态代数的反代数A是拟遗传代数,而且代数A的△好模范畴与Mat(K,M)等价.本文基于双模问题的tame定理,证明了如果由上三角双模问题所对应的拟遗传代数A是△-tame表示型的,则F(△)具有齐次性质,即F(△)中的几乎所有的模都同构于它的Auslander-Reiten变换;进一步地,如果(K,M,H)是上三角双分双模问题,则A是△-tame表示型的当且仅当F(△)具有齐次性质.     

Δ-tame拟遗传代数

设(K,M,H)是上三角双模问题,Brüstle和Hille证明了(K,M,H)的矩阵范畴Mat(K,M)的投射生成子P的自同态代数的反代数A是拟遗传代数,而且代数A的Δ好模范畴与Mat(K,M)等价．本文基于双模问题的tame定理,证明了如果由上三角双模问题所对应的拟遗传代数A是Δ-tame表示型的,则F(Δ)具有齐次性质,即F(Δ)中的几乎所有的模都同构于它的Auslander-Reiten变换;进一步地,如果(K,M,H)是上三角双分双模问题,则A是Δ-tame表示型的当且仅当F(Δ)具有齐次性质．     

Fibonacci代数的Hochschild上同调群

设∧d是Fibonacci代数,基于对Bardzell极小投射双模分解的细致分析,用组合的方法清晰地计算了Fibonacci代数∧d的各阶Hochschild上同调群的维数.     

Fibonacci代数的Hochschild同调群

设Λd是Fibonacci代数,基于对Bardzell极小投射双模分解的细致分析,用组合的方法清晰地计算了Fibonacci代数Λd的各阶Hochschild同调群的维数.     

Fibonacci代数的Hochschild上同调群

设Λ_d是Fibonacci代数,基于对Bardzell极小投射双模分解的细致分析,用组合的方法清晰地计算了Fibonacci代数Λ_d的各阶Hochschild上同调群的维数．     

Δ-tame拟遗传代数

设(K, M, H)是上三角双模问题, Brüstle 和Hille证明了(K, M, H)的矩阵范畴Mat((K, M)的投射生成子P 的自同态代数的反代数A是拟遗传代数, 而且代数A的Δ 好模范畴与Mat((K, M)等价. 本文基于双模问题的tame定理, 证明了如果由上三角双模问题所对应的拟遗传代数A是Δ-tame表示型的, 则 F(Δ)具有齐次性质, 即F(Δ)中的几乎所有的模都同构于它的Auslander-Reiten变换; 进一步地, 如果(K, M, H)是上三角双分双模问题, 则A是Δ-tame表示型的当且仅当 F(Δ)具有齐次性质.     

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．     

T(2,2,2,2)型tubular代数的合成代数

设A为有限域上的T(2,2,2,2)型tubular代数,它是tame遗传代数A0的单点扩张,也是tame遗传代数A∞的单点余扩张．记P0为预投射A0-模集合,L∞是预内射A∞-模集合,则P0,L∞(?)mod A记T=mod A＼(P0∪L∞)．本文证明A的合成代数C(A)具有形为P0·J·L∞的三角分解．     

Morita 型稳定等价下的模- 相对Hochschild (上) 同调

Ardizzoni, Brzeziński 和Menini 在研究代数的形式光滑性以及形式光滑双模时利用相对右导出函子引入了模- 相对Hochschild 上同调的概念. 本文利用相对左导出函子相应地给出模- 相对Hochschild 同调的定义, 讨论了在Morita 型稳定等价下, 代数的Hochschild (上) 同调、相对Hochschild (上) 同调以及模- 相对Hochschild (上) 同调三者之间的关系, 证明了模- 相对Hochschild 同调与上同调是Morita 型稳定等价下的不变量. 作为该结果的应用, 我们得到形式光滑双模与可分双模的一种构造方法, 并给出了通常意义下的Hochschild (上) 同调是Morita 型稳定等价不变量的一种新的证明.     

△-tame quasi-hereditary algebras

Let (K, M, H) be an upper triangular bimodule problem. Brüstle and Hille showed that the opposite algebra A of the endomorphism algebra of a projective generator P of the matrices category of (K, M, H) is quasi-hereditary, and there is an equivalence between the category of △-good modules of A and Mat(K, M). In this note, based on the tame theorem for bimodule problems, we show that if the algebra A associated with an upper triangular bimodule problem is of △-tame representation type, then the category F(△) has the homogeneous property, i.e. almost all modules in F(△) are isomorphic to their Auslander-Reiten translations. Moreover, if (K, M, H) is an upper triangular bipartite bimodule problem, then A is of △-tame representation type if and only if F(△) is homogeneous.     

Noninjectivity of the Predual Bimodule of the Measure Algebra for Infinite Discrete Groups

In this paper, it is proved that the predual bimodule of the measure algebra of an infinite discrete group is not injective despite the fact that the measure algebra of an amenable group is amenable in the sense of Connes. Thus the well-known result of Khelemskii (claiming that, for a von Neumann algebra, Connes-amenability is equivalent to the condition that the predual bimodule is injective) cannot be extended to measure algebras. Moreover, for a discrete amenable group, we give a simple formula for a normal virtual diagonal of the measure algebra. It is shown that a certain canonical bimodule over the measure algebra is not normal.     

The dimension of the tensor algebra of a projective bimodule

It is proved that the dimension of the tensor algebra of a bimodule which is projective with one of the sides differs from the dimension of the ring over which this bimodule is considered by not more than one. A criterion for these dimensions to coincide is given.     

Hochschild Homology of Tame Hecke Algebras

Let A be a tame Hecke algebra of type A. A new minimal projective bimodule resolution for A is constructed and the dimensions of all the Hochschild homology groups and cyclic homology groups are calculated explicitly.     

一个Cluster-Tilted代数的Hochschild上同调环

基于Furuya构造的一个cluster-tilted代数的极小投射双模分解,定义了该投射分解的所谓"余乘"结构,从而证明了该代数的Hochschild上同调环的cup积本质上是平行路的毗连并由此得到了该代数的Hochschild上同调环的一个由生成元与关系给出的实现.     

On the generalized derivations of bimodules

Recently, we introduced the notion of a generalized derivation from a bimodule to a bimodule. In this paper, we give a more general notion based on commutators which covers generalized derivations as a special case. Using it, we show that the separability of an algebra extension is characterized by generalized derivations.     

Bimodule herds

The notion of a bimodule herd is introduced and studied. A bimodule herd consists of a B-A bimodule, its formal dual, called a pen, and a map, called a shepherd, which satisfies unitality and coassociativity conditions. It is shown that every bimodule herd gives rise to a pair of corings and coactions. If, in addition, a bimodule herd is tame i.e. it is faithfully flat and a progenerator, or if it is a progenerator and the underlying ring extensions are split, then these corings are associated to entwining structures; the bimodule herd is a Galois comodule of these corings. The notion of a bicomodule coherd is introduced as a formal dualisation of the definition of a bimodule herd. Every bicomodule coherd defines a pair of (non-unital) rings. It is shown that a tame B-A bimodule herd defines a bicomodule coherd, and sufficient conditions for the derived rings to be isomorphic to A and B are discussed. The composition of bimodule herds via the tensor product is outlined. The notion of a bimodule herd is illustrated by the example of Galois co-objects of a commutative, faithfully flat Hopf algebra.     

Hochschild cohomology of Möbius algebras

The additive structure of the Hochschild cohomology ring for a Möbius algebra is described. We use the structure of the bimodule minimal projective resolution of the algebra, constructed in a previous paper. Bibliography: 4 titles.