共查询到20条相似文献,搜索用时 15 毫秒
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Oblatum 10-VII-1993 & 26-IX-1994 相似文献
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Given an algebra A, we associate an incidence algebra A() andcompare their Hochschild cohomology groups. 相似文献
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Steffen Koenig 《Journal of Pure and Applied Algebra》2009,213(5):886-891
Suppose B is an algebra with a stratifying ideal BeB generated by an idempotent e. We will establish long exact sequences relating the Hochschild cohomology groups of the three algebras B, B/BeB and eBe. This provides a common generalization of various known results, all of which extend Happel’s long exact sequence for one-point extensions. Applying one of these sequences to Hochschild cohomology algebras modulo the ideal generated by homogeneous nilpotent elements shows, in some cases, that these algebras are finitely generated. 相似文献
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We show that certain tiled R-orders
$\Lambda$ have periodic projective resolutions and hence we determine the Hochschild
cohomology ring of $\Lambda$. This generalises, reproves and connects
several results in the literature.Received: 23 October 2002 相似文献
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We consider the polynomial algebra \({\mathbb{C}[{\bf z}] := \mathbb{C}[z_1, z_2, z_3]}\) and the polynomial \({f := z^{3}_{1} + z^3_2 + z^3_3 + 3qz_1z_2z_3}\), where \({q \in \mathbb{C}}\). Our aim is to compute the Hochschild homology and cohomology of the cubic surface \({\mathcal{X}_f := \{{\bf z} \in \mathbb{C}^3/f({\bf z}) = 0\}}\). For explicit computations, we shall make use of a method suggested by M. Kontsevich. Then, we shall develop it in order to determine the Hochschild homology and cohomology by means of multivariate division and Groebner bases. Some formal computations with Maple are also used. 相似文献
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In this paper we prove that on a smooth algebraic variety the HKR-morphism twisted by the square root of the Todd genus gives an isomorphism between the sheaf of poly-vector fields and the sheaf of poly-differential operators, both considered as derived Gerstenhaber algebras. In particular we obtain an isomorphism between Hochschild cohomology and the cohomology of poly-vector fields which is compatible with the Lie bracket and the cupproduct. The latter compatibility is an unpublished result by Kontsevich.Our proof is set in the framework of Lie algebroids and so applies without modification in much more general settings as well. 相似文献
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Let E be a long exact sequence of modules over an algebra A admitting a contracting homotopy over a subalgebra B ⊂ A. In settings
of relative homological algebra, the Hochschild cocycle corresponding to the sequence E is described explicitly. The “absolute
case” has been earlier investigated by V. Dlab and C. M. Ringel. Applied to that case, the present investigation provides
shorter arguments than those of Dlab and Ringel. Bibliography: 3 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 330, 2006, pp. 29–35. 相似文献
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Jorge A. Guccione Juan J. Guccione 《Proceedings of the American Mathematical Society》2004,132(5):1241-1250
Let be a field, a finite-dimensional Frobenius -algebra and , the Nakayama automorphism of with respect to a Frobenius homomorphism . Assume that has finite order and that has a primitive -th root of unity . Consider the decomposition of , obtained by defining , and the decomposition of the Hochschild cohomology of , obtained from the decomposition of . In this paper we prove that and that if the decomposition of is strongly -graded, then acts on and .
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Anne V. Shepler Sarah Witherspoon 《Transactions of the American Mathematical Society》2008,360(8):3975-4005
We develop and collect techniques for determining Hochschild cohomology of skew group algebras and apply our results to graded Hecke algebras. We discuss the explicit computation of certain types of invariants under centralizer subgroups, focusing on the infinite family of complex reflection groups to illustrate our ideas. Resulting formulas for Hochschild two-cocycles give information about deformations of and, in particular, about graded Hecke algebras. We expand the definition of a graded Hecke algebra to allow a nonfaithful action of on , and we show that there exist nontrivial graded Hecke algebras for , in contrast to the case of the natural reflection representation. We prove that one of these graded Hecke algebras is equivalent to an algebra that has appeared before in a different form.
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We interpret Hochschild cohomology as the Lie algebra of the derived Picard group and deduce that it is preserved under derived equivalences. 相似文献
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Hochschild cohomology of truncated basic cycle 总被引:9,自引:0,他引:9
Pu Zhang 《中国科学A辑(英文版)》1997,40(12):1272-1278
Dimensions of the Hochschild cohomology groups of a truncated algebra of a basic cycle are explicitly given.
Project supported by the State Education Commission of China, the Chinese Academy of Sciences and the National Natural Science
Foundation of China. 相似文献
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Yun-ge XU Yang HAN & Wen-feng JIANG Faculty of Mathematics & Computer Science Hubei University Wuhan China Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2007,50(5):727-736
For a truncated quiver algebra over a field of an arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its global dimension is finite if and only if its quiver has no oriented cycles. 相似文献
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基于Buchweitz等人对Koszul代数的Hochschild上同调环的乘法结构的细致分析,给出了Koszul代数的Hochschild上同调环的乘法本质上是平行路的毗连的一个充要条件,并由此重新证明了二次三角string代数的Hochschild上同调环的乘法是平凡的,从而改进了Bustamante的证明. 相似文献
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Thorsten Holn 《代数通讯》2013,41(11):3625-3646
The aim of this paper is to study the structure of the Hochschild cohomology ring of Brauer tree algebras. We explicitly describe the even cohomology ring by generators and relations. This generalizes results of [11] on the Hochschild cohomology of blocks of modular group algebras with cyclic defect groups. 相似文献
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Hochschild cohomology of special biserial algebras 总被引:1,自引:0,他引:1
Yun-ge Xu 《中国科学A辑(英文版)》2007,50(8):1117-1128
Based on a four-term exact sequence,the formulae on the dimensions of the first and the second Hochschild cohomology groups of special biserial algebras with normed bases are obtained in terms of combinatorics. 相似文献