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- W2116325133 abstract "If A is a cocommutative algebra with coproduct, then so is the smash product algebra of a symmetric algebra SymV with A, where V is an A-module. Such smash product algebras, with A a group ring or a Lie algebra, have been deformed by Drinfel'd and more recently, Crawley-Boevey and Holland, Etingof and Ginzburg (and Gan), and others. These algebras include symplectic reection algebras and innitesimal Hecke algebras. We introduce a family of deformations H of the smash product algebras mentioned at the beginning of the abstract, by deforming the relations V ^ V. Thus : V ^ V ! A V ; we characterize the 's for which the PBW property holds. We then analyse in detail the case where A = NCW is the nilCoxeter algebra, and : V ^V ! A. In the case where A is a cocommutative Hopf algebra, that is A-compatible, is equivalent to some other conditions - that is an A- module map, or the Yetter-Drinfeld condition. We examine what further conditions are needed on to achieve a Hopf algebra structure on the de- formed algebra (with V primitive). Finally, we provide a Hopf-theoretic analogue of symplectic reections." @default.
- W2116325133 created "2016-06-24" @default.
- W2116325133 creator A5059899589 @default.
- W2116325133 date "2007-05-15" @default.
- W2116325133 modified "2023-09-27" @default.
- W2116325133 title "DRINFELD-HECKE ALGEBRAS OVER COCOMMUTATIVE ALGEBRAS" @default.
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