共查询到20条相似文献，搜索用时 0 毫秒
1.
Daiki Obara 《代数通讯》2013,41(8):3545-3587
We consider quiver algebras A q over a field k defined by two cycles and a quantum-like relation depending on a nonzero element q in k. We determine the Hochschild cohomology ring of A q and give necessary and sufficient conditions for A q to have the finitely generated Hochschild cohomology ring. 相似文献
2.
In this article we show that an algebra A = K Γ/(f(X s )) has a periodic projective bimodule resolution of period 2, where KΓ is the path algebra of the circular quiver Γ with s vertices and s arrows over a commutative ring K, f(x) is a monic polynomial over K and X is the sum of all arrows in KΓ. Moreover, by means of this projective bimodule resolution, we compute the Hochschild cohomology group of A, and we give a presentation of the Hochschild cohomology ring HH?(A) by the generators and the relations in the case K is a field. 相似文献
3.
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． 相似文献
4.
设A是有限表示型遗传代数A=kQ的投射模范畴proj A上的根双模rad(-,-)所对应的拟遗传代数,基于Bardzell构造的极小投射双模分解,A的各阶Hochschild上同调群的维数被清晰地计算． 相似文献
5.
We show how to compute the low Hochschild cohomology groups of a partial relation extension algebra. 相似文献
6.
范金梅 《纯粹数学与应用数学》2010,26(2):241-250
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. 相似文献
7.
Stanislaw Betley 《代数通讯》2013,41(2):576-587
We calculate Hochschild cohomology groups of the integers treated as an algebra over so-called field with one element. We compare our results with calculation of the topological Hochschild cohomology groups of the integers—this is the case when one considers integers as an algebra over the sphere spectrum. 相似文献
8.
Daiki OBARA 《Frontiers of Mathematics in China》2016,11(4):1003-1015
We consider a one point extension algebra B of a quiver algebra A q over a field k defined by two cycles and a quantum-like relation depending on a nonzero element q in k. We determine the Hochschild cohomology ring of B modulo nilpotence and show that if q is a root of unity, then B is a counterexample to Snashall-Solberg’s conjecture. 相似文献
9.
Michel van den Bergh 《K-Theory》1994,8(3):213-230
We compute the Hochschild and cyclic homology of certain three-dimensional quantum spaces (type A algebras), introduced by Artin and Schelter. We show that the Hochschild homology is determined by the quasi-classical limit. 相似文献
10.
We use (non-)additive sheaves to introduce an (absolute) notion of Hochschild cohomology for exact categories as Ext's in a suitable bisheaf category. We compare our approach to various definitions present in the literature. 相似文献
11.
Ali N. A. Koam 《代数通讯》2018,46(7):2947-2963
In this paper, our goal is to develop the equivariant version of Hochschild cohomology. In particular, we develop a cohomology theory for oriented algebras. 相似文献
12.
María Andrea Gatica 《代数通讯》2013,41(6):2039-2056
The purpose of this article is to present some computations of Hochschild cohomology groups of particular classes of incidence algebras using one-point extensions and one-point coextensions. 相似文献
13.
Liran Shaul 《代数通讯》2013,41(7):2898-2907
Let be a regular ring, and let A, B be essentially finite type -algebras. For any functor F: D(ModA) × ? × D(ModA) → D(ModB) between their derived categories, we define its twist F!: D(ModA) × ? × D(ModA) → D(ModB) with respect to dualizing complexes, generalizing Grothendieck's construction of f!. We show that relations between functors are preserved between their twists, and deduce that various relations hold between derived Hochschild (co)-homology and the f! functor. We also deduce that the set of isomorphism classes of dualizing complexes over a ring (or a scheme) form a group with respect to derived Hochschild cohomology, and that the twisted inverse image functor is a group homomorphism. 相似文献
14.
Magnus Hellstrøm-Finnsen 《代数通讯》2013,41(12):5202-5233
We define the Hochschild complex and cohomology of a ring object in a monoidal category enriched over abelian groups. We interpret the cohomology groups and prove that the cohomology ring is graded-commutative. 相似文献
15.
Hochschild （Co）homology of a Class of Nakayama Algebras 总被引：1，自引：0，他引：1
Yun Ge XU Dan WANG 《数学学报(英文版)》2008,24(7):1097-1106
16.
Ronald G. Douglas 《Journal of Functional Analysis》2011,261(12):3723-3734
We show that every finitely generated group admits weak analogues of an invariant expectation, whose existence characterizes exact groups. This fact has a number of applications. We show that Hopf G-modules are relatively injective, which implies that bounded cohomology groups with coefficients in all Hopf G-modules vanish in all positive degrees. We also prove a general fixed point theorem for actions of finitely generated groups on ?∞-type spaces. Finally, we define the notion of weak exactness for certain Banach algebras. 相似文献
17.
18.
Takao Hayami 《代数通讯》2013,41(7):2785-2803
We will give an efficient bimodule projective resolution of an order Γ, where Γ is an order of a simple component of the rational group ring ? Q 2 r of the generalized quaternion 2-group Q 2 r of order 2 r+2. Moreover, we will determine the ring structure of the Hochschild cohomology HH*(Γ) by calculating the Yoneda products using this bimodule projective resolution. 相似文献
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20.
《Journal of Pure and Applied Algebra》2022,226(7):106903
We calculate the Gerstenhaber bracket on Hopf algebra and Hochschild cohomologies of the Taft algebra for any integer which is a nonquasi-triangular Hopf algebra. We show that the bracket is indeed zero on Hopf algebra cohomology of , as in all known quasi-triangular Hopf algebras. This example is the first known bracket computation for a nonquasi-triangular algebra. Also, we find a general formula for the bracket on Hopf algebra cohomology of any Hopf algebra with bijective antipode on the bar resolution that is reminiscent of Gerstenhaber's original formula for Hochschild cohomology. 相似文献