Mathematics > Rings and Algebras
This paper has been withdrawn by Apoorva Khare
[Submitted on 15 May 2007 (v1), last revised 20 Jan 2016 (this version, v2)]
Title:Drinfeld-Hecke algebras over cocommutative algebras
No PDF available, click to view other formatsAbstract:If A is a cocommutative algebra with coproduct, then so is the smash product algebra of a symmetric algebra Sym(V) with A, where V is an A-module. Such smash product algebras, with A a group ring or a Lie algebra, have families of deformations that have been studied widely in the literature; examples include symplectic reflection algebras and infinitesimal Hecke algebras. We introduce a family of deformations of these smash product algebras for general A, and characterize the PBW property. We then characterize the Jacobi identity for "grouplike" algebras (that include group rings and the nilCoxeter algebra), and precisely identify the PBW deformations in the example where A is the nilCoxeter algebra. We end with the more prominent case - where A is a Hopf algebra. We show the equivalence of several versions of the "deformed" relations in the smash product, and identify the PBW deformations which are Hopf algebras as well.
Submission history
From: Apoorva Khare [view email][v1] Tue, 15 May 2007 01:33:19 UTC (34 KB)
[v2] Wed, 20 Jan 2016 04:14:52 UTC (1 KB) (withdrawn)
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