Biproducts and Two-Cocycle Twists of Hopf Algebras

2006/03/11 by David E. Radford, Hans-Jürgen Schneider, Radford, David E. +1
Mathematics · #16W30 #17B10 #17B37 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16W30 #msc:17B10 #msc:17B37

paper · pdf · doi:10.48550/arxiv.math/0603267

amstex, 29 pages

arxiv created 2006/03/11 · arxiv updated 2009/12/01

Abstract

Let H be a Hopf algebra with bijective antipode over a field k and suppose that R#H is a bi-product. Then R is a bialgebra in the Yetter--Drinfel'd category _H^H\mathcal YD. We describe the bialgebras (R#H)^op and (R#H)^o explicitly as bi-products R^\UOP#H^op and R^\UO#H^o respectively where R^\UOP is a bialgebra in ^H^op_H^op\mathcal YD and R^\UO is a bialgebra in ^Ho_H^o\mathcal YD. We use our results to describe two-cocycle twist bialgebra structures on the tensor product of bi-products.

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