共查询到20条相似文献,搜索用时 441 毫秒
1.
I. A. Dolguntseva 《Algebra and Logic》2007,46(6):373-384
We introduce the concept of Hochschild cohomologies for associative conformal algebras. It is shown that the second cohomology
group of a conformal Weyl algebra with values in any bimodule is trivial. As a consequence, we derive that the conformal Weyl
algebra is segregated in any extension with nilpotent kernel.
Supported by RFBR grant No. 05-01-00230 and via SB RAS Integration project No. 1.9.
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Translated from Algebra i Logika, Vol. 46, No. 6, pp. 688–706, November–December, 2007. 相似文献
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Given a generalized Weyl algebra A of degree 1 with the base algebra D, we prove that the difference of the Gelfand–Kirillov dimension of A and that of D could be any positive integer or infinity. Under mild conditions, this difference is exactly 1. As applications, we calculate the Gelfand–Kirillov dimensions of various algebras of interest, including the (quantized) Weyl algebras, ambiskew polynomial rings, noetherian (generalized) down-up algebras, iterated Ore extensions, quantum Heisenberg algebras, universal enveloping algebras of Lie algebras, quantum GWAs, etc. 相似文献
4.
Lieven Le Bruyn 《代数通讯》2013,41(3):865-876
In this note we describe two simple tricks derived from work of M. Artin , J. Tate and M. Van den Bergh [2] and apply them to the quantum enveloping algebra discovered by E. Witten [ll] encoding duality in three dimensional Chern-Simons gauge theory with structure group SU(2). In particular, we give a more conceptual interpretation of the dichotony in the representation theory and determine all finite dimensional simple representations. 相似文献
5.
Nicolas Marconnet 《Comptes Rendus Mathematique》2004,338(2):117-120
Hochschild homology of cubic Artin–Schelter regular algebras of type A with generic coefficients is computed. We follow the method used by Van den Bergh (K-Theory 8 (1994) 213–230) in the quadratic case, by considering these algebras as deformations of a polynomial algebra, with remarkable Poisson brackets. A new quasi-isomorphism is introduced. De Rham cohomology, cyclic and periodic cyclic homologies, and Hochschild cohomology are also computed. To cite this article: N. Marconnet, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
6.
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
7.
The automorphism groups of algebras are found in many papers. Using auto-invariance, we find the automorphism groups of the
Laurent extension of the polynomial ring and the quantum n-plane (respectively, twisting polynomial ring) in this work. As an application of the results of this work, we can find the
automorphism group of a twisting algebra. We define a generalized Weyl algebra and show that the generalized Weyl algebra
is simple. We also find the automorphism group of a generalized Weyl algebra. We show that the generalized Weyl algebra A
m,m+n
is the universal enveloping algebra of the generalized Witt algebra W(m,m + n).
This work was supported by 2007 Research fund of Hanyang University 相似文献
8.
In this paper we present a new approach to Grothendieck duality over commutative rings. Our approach is based on the idea
of rigid dualizing complexes, which was introduced by Van den Bergh in the context of noncommutative algebraic geometry. The
method of rigidity was modified to work over general commutative base rings in our paper (Yekutieli and Zhang, Trans AMS 360:3211–3248,
2008). In the present paper we obtain many of the important local features of Grothendieck duality, yet manage to avoid lengthy
and difficult compatibility verifications. Our results apply to essentially finite type algebras over a regular noetherian
finite dimensional base ring, and hence are suitable for arithmetic rings. In the sequel paper (Yekutieli, Rigid dualizing
complexes on schemes, in preparation) these results will be used to construct and study rigid dualizing complexes on schemes.
This research was supported by the US–Israel Binational Science Foundation. The second author was partially supported by the
US National Science Foundation. 相似文献
9.
In this work, we introduce the point parameter ring B, a generalized twisted homogeneous coordinate ring associated to a degenerate version of the three-dimensional Sklyanin algebra. The surprising geometry of these algebras yields an analogue to a result of Artin–Tate–van den Bergh, namely that B is generated in degree one and thus is a factor of the corresponding degenerate Sklyanin algebra. 相似文献
10.
The Koszul property was generalized to homogeneous algebras of degree in [5], and related to -complexes. We show that if the -homogeneous algebra is generalized Koszul, AS-Gorenstein and of finite global dimension, then one can apply the Van den Bergh duality theorem to i.e., there is a Poincaré duality between Hochschild homology and cohomology of as for . 相似文献
11.
《Journal of Algebra》2006,295(1):141-156
Stephenson and Vancliff recently introduced two families of quantum projective 3-spaces (quadratic and Artin–Schelter regular algebras of global dimension 4) which have the property that the associated automorphism of the scheme of point modules is finite order, and yet the algebra is not finite over its center. This is in stark contrast to theorems of Artin, Tate, and Van den Bergh in global dimension 3. We analyze the representation theory of these algebras. We classify all of the finite-dimensional simple modules and describe some zero-dimensional elements of Proj, i.e., so called fat point modules. In particular, we observe that the shift functor on zero-dimensional elements of Proj, which is closely related to the above automorphism, actually has infinite order. 相似文献
12.
We introduce and study a large class of algebras with triangular decomposition which we call braided doubles. Braided doubles provide a unifying framework for classical and quantum universal enveloping algebras and rational Cherednik algebras. We classify braided doubles in terms of quasi-Yetter-Drinfeld (QYD) modules over Hopf algebras which turn out to be a generalisation of the ordinary Yetter-Drinfeld modules. To each braiding (a solution to the braid equation) we associate a QYD-module and the corresponding braided Heisenberg double—this is a quantum deformation of the Weyl algebra where the role of polynomial algebras is played by Nichols-Woronowicz algebras. Our main result is that any rational Cherednik algebra canonically embeds in the braided Heisenberg double attached to the corresponding complex reflection group. 相似文献
13.
14.
Tim Cramer 《Advances in Mathematics》2010,224(3):1097-1120
We show that the reduced Drinfeld double of the Ringel-Hall algebra of a hereditary category is invariant under derived equivalences. By associating an explicit isomorphism to a given derived equivalence, we also extend the results of Burban and Schiffmann [5] and [006], Sevenhant and Van den Bergh (1999) [25], and Xiao and Yang (2001) [31]. 相似文献
15.
Kok-Ming Teo 《代数通讯》2013,41(9):3027-3035
In their recent paper [13], Tate and Van den Bergh studied certain quadratic algebras, called the “Sklyanin algebras”. They proved that these algebras have the Hilbert series of a polynomial algebra, are Noetherian and Koszul, and satisfy the Auslander-Gorenstein and Cohen-Macaulay conditions. This paper gives an alternative proof of these results, as suggested in [13], and thereby answering a question in their paper. 相似文献
16.
Luc Menichi 《K-Theory》2004,32(3):231-251
We show that the Connes–Moscovici negative cyclic cohomology of a Hopf algebra equipped with a character has a Lie bracket of degree -2. More generally, we show that a cyclic operad with multiplication is a cocyclic module whose simplicial cohomology is a Batalin–Vilkovisky algebra and whose negative cyclic cohomology is a graded Lie algebra of degree -2. This generalizes the fact that the Hochschild cohomology algebra of a symmetric algebra is a Batalin–Vilkovisky algebra. 相似文献
17.
By using the Ringel-Hall algebra approach we first present a new proof of Kac's theorem for species over a finite field. The method used here is quite different from earlier techniques. In [SV] Sevenhant and Van den Bergh have discovered an interesting relation between a conjecture of Kac on representations of quivers and the structure of the Ringel-Hall algebras in some special cases. We second show that this relation still holds for species.
The research was supported in part by the NSF of China and the TRAPOYP. 相似文献
18.
The authors first construct an explicit minimal projective bimodule resolution(P, δ) of the Temperley-Lieb algebra A, and then apply it to calculate the Hochschild cohomology groups and the cup product of the Hochschild cohomology ring of A based on a comultiplicative map Δ:P → PAP. As a consequence, the authors determine the multiplicative structure of Hochschild cohomology rings of both Temperley-Lieb algebras and representation-finite q-Schur algebras under the cup product by giving an explicit presentation by generators and relations. 相似文献
19.
Ulrich Krähmer 《Israel Journal of Mathematics》2012,189(1):237-266
The recent result of Brown and Zhang establishing Poincaré duality in the Hochschild (co)homology of a large class of Hopf algebras is extended to right coideal subalgebras over which the Hopf algebra is faithfully flat, and applied to the standard Podle? quantum 2-sphere. 相似文献
20.
We construct a generic Hall algebra of the Kronecker algebra and prove that its twisted version is a polynomial algebra in infinitely many variables over the twisted generic composition algebra. The variables are explicitly given as some central elements in the generic Hall algebra. Thus, we obtain generic versions in the Kronecker case of theorems by Hua-Xiao and Sevenhant-Van den Bergh. 相似文献