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- W4297819345 abstract "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." @default.
- W4297819345 created "2022-10-01" @default.
- W4297819345 creator A5059899589 @default.
- W4297819345 date "2007-05-14" @default.
- W4297819345 modified "2023-10-18" @default.
- W4297819345 title "Drinfeld-Hecke algebras over cocommutative algebras" @default.
- W4297819345 doi "https://doi.org/10.48550/arxiv.0705.2067" @default.
- W4297819345 hasPublicationYear "2007" @default.
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