L-R smash products for bimodule algebras

In this paper, we prove that the L-R smash product A (＃)H is exactly the twisted smash product A * H if H is a finite dimensional cocommutative Hopf algebra, and give a sufficient and necessary condition for L-R smash products to be bialgebras (Hopf algebras). For any finite dimensional coquasitriangular Hopf algebra (H, σ), we prove that the L-R smash product H (＃)H is semisimple Artinian if H is semisimple and H* is unimodular. In particular, the L-R smash product D(H) * (＃)D(H) * semisimple Artinian if the Drinfel' d double D(H) is semisimple.

作 者： ZHANG Liangyun   作者單位： Department of Mathematics, Nanjing Agricultural University, Nanjing 210095, China;Department of Mathematics, Nanjing University, Nanjing 210008, China  刊 名： 自然科學(xué)進展（英文版）  SCI 英文刊名： PROGRESS IN NATURAL SCIENCE  年，卷(期)： 2006 16(6)  分類號： N1  關(guān)鍵詞： bimodule algebras   L-R smash products   coquasitriangular Hopf algebras   Long bialgebras  

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