Classification of twisted generalized Weyl algebras over polynomial rings

JOURNAL OF ALGEBRA

卷:546

Article

Hartwig, Jonas T.¹  Rosso, Daniele² 

[1] Iowa State Univ, Dept Math, Ames, IA 50011 USA

[2] Indiana Univ Northwest, Dept Math & Actuarial Sci, Gary, IN 46408 USA

关键词: Generalized Weyl algebras;    Twisted generalized Weyl algebras;   

DOI  :  10.1016/j.jalgebra.2019.10.045

来源: Elsevier

【 摘 要 】

Let R be a polynomial ring in m variables over a field of characteristic zero. We classify all rank n twisted generalized Weyl algebras over R, up to Z(n)-graded isomorphisms, in terms of higher spin 6-vertex configurations. Examples of such algebras include infinite-dimensional primitive quotients of U(g) where g = gl(n) sl(n), or sp(2n), algebras related to U((sl) over cap (2)) and a finite W-algebra associated to Sl(4). To accomplish this classification we first show that the problem is equivalent to classifying solutions to the binary and ternary consistency equations. Secondly, we show that the latter problem can be reduced to the case n = 2, which can be solved using methods from previous work by the authors [17], [15]. As a consequence we obtain the surprising fact that (in the setting of the present paper) the ternary consistency relation follows from the binary consistency relation. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free