共查询到20条相似文献,搜索用时 15 毫秒
1.
Let A≡KΔ /I be a factor of a path algebra. We develop a strategy to compute dim H
1(A), the dimension of the first Hochschild cohomology group of A, using combinatorial data from (Δ,I). That allows us to connect dim H
1(A) with the rank and p-rank of the fundamental group π1(Δ,I) of (Δ,I). We get explicit formulae for dim H
1(A), when every path in Δ parallel to an arrow belongs to I or when I is homogeneous.
Received: 12 April 1999 / Revised version: 9 October 2000 相似文献
2.
We prove that, as Gerstenhaber algebras, the Hochschild cohomology ring of the tensor product of two algebras is isomorphic to the tensor product of the respective Hochschild cohomology rings of these two algebras, when at least one of them is finite dimensional. In case of finite dimensional symmetric algebras, this isomorphism is an isomorphism of Batalin–Vilkovisky algebras. As an application, we explain by examples how to compute the Batalin–Vilkovisky structure, in particular, the Gerstenhaber Lie bracket, over the Hochschild cohomology ring of the group algebra of a finite abelian group. 相似文献
3.
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
4.
Mitja Mastnak 《Journal of Pure and Applied Algebra》2009,213(7):1399-1417
We give explicit formulas for maps in a long exact sequence connecting bialgebra cohomology to Hochschild cohomology. We give a sufficient condition for the connecting homomorphism to be surjective. We apply these results to compute all bialgebra two-cocycles of certain Radford biproducts (bosonizations). These two-cocycles are precisely those associated to the finite dimensional pointed Hopf algebras in the recent classification of Andruskiewitsch and Schneider, in an interpretation of these Hopf algebras as graded bialgebra deformations of Radford biproducts. 相似文献
5.
Bertin Diarra Fana Tangara 《P-Adic Numbers, Ultrametric Analysis, and Applications》2009,1(2):128-135
Let q be a principal unit of the ring of valuation of a complete valued field K, extension of the field of p-adic numbers. Generalizing Mahler basis, K. Conrad has constructed orthonormal basis, depending on q, of the space of continuous functions on the ring of p-adic integers with values in K. Attached to q there are two models of the quantum plane and a model of the quantum Weyl algebra, as algebras of bounded linear operators
on the space of p-adic continuous functions. For q not a root of unit, interesting orthonormal (orthogonal) families of these algebras are exhibited and providing p-adic completion of quantum plane and quantum Weyl algebras.
The text was submitted by the authors in English. 相似文献
6.
Juan Carlos Bustamante 《Journal of Pure and Applied Algebra》2006,204(3):616-626
We show that the graded commutative ring structure of the Hochschild cohomology HH*(A) is trivial in case A is a triangular quadratic string algebra. Moreover, in case A is gentle, the Lie algebra structure on HH*(A) is also trivial. 相似文献
7.
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
8.
9.
10.
S.J. Witherspoon 《Advances in Mathematics》2004,185(1):136-158
We give a general construction of rings graded by the conjugacy classes of a finite group. Some examples of our construction are the Hochschild cohomology ring of a finite group algebra, the Grothendieck ring of the Drinfel'd double of a group, and the orbifold cohomology ring for a global quotient. We generalize the first two examples by deriving product formulas for the Hochschild cohomology ring of a group crossed product and for the Grothendieck ring of an abelian extension of Hopf algebras. Our results account for similarities in the product structures among these examples. 相似文献
11.
Fethi Bouzeffour 《Journal of Mathematical Analysis and Applications》2007,336(2):833-848
We study fractional transforms associated with q-Bessel operator which is useful to inverse q-Riemann-Liouville and q-Weyl transforms. 相似文献
12.
13.
We compute the Hochschild cohomology groups HH?(A) in case A is a triangular string algebra, and show that its ring structure is trivial. 相似文献
14.
15.
Motivated by Weyl algebra analogues of the Jacobian conjecture and the tame generators problem, we prove quantum versions of these problems for a family of analogues to the Weyl algebras. In particular, our results cover the Weyl–Hayashi algebras and tensor powers of a quantization of the first Weyl algebra which arises as a primitive factor algebra of . 相似文献
16.
Van C. Nguyen Xingting Wang Sarah Witherspoon 《Journal of Pure and Applied Algebra》2019,223(1):316-339
Over a field of prime characteristic , we prove that the cohomology rings of some pointed Hopf algebras of dimension are finitely generated. These are Hopf algebras arising in the ongoing classification of finite dimensional pointed Hopf algebras in positive characteristic. They include bosonizations of Nichols algebras of Jordan type in a general setting. When , we also consider their Hopf algebra liftings, that is Hopf algebras whose associated graded algebra with respect to the coradical filtration is given by such a bosonization. Our proofs are based on an algebra filtration and a lemma of Friedlander and Suslin, drawing on both twisted tensor product resolutions and Anick resolutions to locate the needed permanent cocycles in May spectral sequences. 相似文献
17.
18.
Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH1(B) with coefficients in the B-B-bimodule B. We find several consequences when B is representation-finite, and also in the case where B is cluster-tilted of type .
M. J. Redondo is a researcher from CONICET, Argentina. 相似文献
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20.
Fei Xu 《Journal of Pure and Applied Algebra》2008,212(11):2555-2569
Let C be a small category and R a commutative ring with identity. The cohomology ring of C with coefficients in R is defined as the cohomology ring of the topological realization of its nerve. First we give an example showing that this ring modulo nilpotents is not finitely generated in general, even when the category is finite EI. Then we study the relationship between the cohomology ring of a category and those of its subcategories and extensions. The main results generalize certain theorems in group cohomology theory. 相似文献