PORTUGALIAE MATHEMATICA Vol. 55, No. 3, pp. 323331 (1998) 

Normal Smash ProductsShilin Yang and Dingguo WangComputer Institute, Beijing Polytechnic University,Beijing 100044  P.R. CHINA Department of Mathematics, Qufu Normal University, Shandong 273165  P.R. CHINA Abstract: Let $H$ be a coFrobenius Hopf algebra over a field $k$ and $A$ a right $H$comodule algebra. It is shown that $A$ is $H$faithful and $A_N\cardinal N^*\in\Phi$ iff $A\cardinal H^{*\rat}\in\Phi$, where $N$ is a subgroup of $G(H)=\{g\in H\, \Delta (g)=g\otimes g\}$ and $A_N$ is $N$coinvariants, $\Phi$ denotes a normal class. It is also shown that if $A/A_1$ is right $H$Galois and $A_1$ is central simple, then so is $A\cardinal H^{*\rat}$. In particular, if $A_1$ is a divisible ring, then $A\cardinal H^{*\rat}$ is a dense ring of linear transformations of the vector space $A$ over $A_1$. Let $H$ be a finite dimensional Hopf algebra over the field $k$ and $A$ an $H$module algebra, $K$ is a unimodular and normal subHopfalgebra and $\overline H=H/K^+H$, it is obtained that $A^K\cardinal \overline H\in\Phi$ and $A$ is $H^*$faithful iff $A\cardinal H\in \Phi$. Keywords: Smash product; normal class; central simple. Classification (MSC2000): 16S40, 16W30 Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
© 1998 Sociedade Portuguesa de Matemática
