Unimodularity of finite dimensional Hopf algebras
Unimodularity of finite dimensional Hopf algebras
复制标题
有限维Hopf代数的幺模性
DOI：
10.21099/tkbjm/1496162995
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发表时间：
1996
影响因子：
0.7
通讯作者：
S. Suzuki
中科院分区：
文献类型：
--
作者：
S. Suzuki
介绍。D. Radford[4]证明了有限维Hopf代数$ a $是对称代数当且仅当(1)$ a $是单模的，且(2)对映对$s^{2}$的平方是内代数自同构。众所周知，Sweedler的四维Hopf代数表明，条件(2)并不一定隐含条件(1)。本文给出了一个例子，证明反之也不成立。
Introduction. D. Radford [4] proved that a finite dimensional Hopf algebra $A$ is a symmetric algebra if and only if (1) $A$ is unimodular, and (2) the square of the antipode $s^{2}$ is an inner algebra-automorphism. It is well-known that the 4-dimensional Hopf algebra of Sweedler shows that Condition (2) does not necessarily imply Condition (1). We present in this paper an example which shows that the converse does not hold either.