Depth one extensions of semisimple algebras and Hopf subalgebras

Details Depth one extensions of semisimple algebras and Hopf subalgebras Depth one extensions of semisimple algebras and Hopf subalgebras

2011-03-03

arxiv.org/abs/1103.0685v1

Mathematics

Quantum Algebra

10 pages, submitted

Scientific paper

An extension of $k$-algebras $B \subset A$ is said to have depth one if there exists a positive integer $n$ such that $ A$ is a direct summand of $ B^n$ in $_B\mtr{Mod}_B$. Depth one extensions of semisimple algebras are completely characterized in terms of their centers. For extensions of semisimple Hopf algebras our results are similar to those obtained for finite group algebra extensions in \cite{BKone}.

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