共查询到20条相似文献，搜索用时 15 毫秒
1.
Daiki Obara 《代数通讯》2013,41(5):1724-1761
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, and describe the minimal projective bimodule resolution of A q . In particular, in the case q = 1, we determine the Hochschild cohomology ring of A 1 and show that it is a finitely generated k-algebra. Moreover the Hochschild cohomology ring of A 1 modulo nilpotence is isomorphic to the polynomial ring of two variables. 相似文献
2.
We show how to compute the low Hochschild cohomology groups of a partial relation extension algebra. 相似文献
3.
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
4.
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
5.
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
6.
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
7.
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
8.
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
9.
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
10.
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
11.
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
12.
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
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《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
16.
《代数通讯》2013,41(10):4871-4897
Abstract In order to study the Hochschild cohomology of an n-triangular algebra 𝒯 n , we construct a spectral sequence, whose terms are parametrized by the length of the trajectories of the quiver associated with 𝒯 n , and which converges to the Hochschild cohomology of 𝒯 n . We describe explicitly its components and its differentials which are sums of cup products. In case n = 3 we study some properties of the differential at level 2. We give some examples of use of the spectral sequence and recover formulas for the dimension of the cohomology groups of particular cases of triangular algebras. 相似文献
17.
Let be a unital Banach algebra. A projection in which is equivalent to the identitity may give rise to a matrix-like structure on any two-sided ideal in . In this set-up we prove a theorem to the effect that the bounded cohomology vanishes for all . The hypotheses of this theorem involve (i) strong H-unitality of , (ii) a growth condition on diagonal matrices in , and (iii) an extension of in by an amenable Banach algebra. As a corollary we show that if is an infinite dimensional Banach space with the bounded approximation property, is an infinite dimensional -space, and is the Banach algebra of approximable operators on , then for all .
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We determine the Hochschild cohomology algebras of the square-free monomial complete intersections. In particular we provide an explicit formula for the cup product which gives the cohomology module an algebra structure and then we describe this structure in terms of generators and relations. In addition, we compute the Hilbert series of the Hochschild cohomology of these algebras. 相似文献
20.
Marco A. Farinati Andrea L. Solotar 《Proceedings of the American Mathematical Society》2004,132(10):2859-2865
We prove that is a Gerstenhaber algebra, where is a Hopf algebra. In case is the Drinfeld double of a finite-dimensional Hopf algebra , our results imply the existence of a Gerstenhaber bracket on . This fact was conjectured by R. Taillefer. The method consists of identifying as a Gerstenhaber subalgebra of (the Hochschild cohomology of ).