On the structure of A/k-bialgebras in prime characteristic

Abstract

In this paper, we study A/k-bialgebras in prime characteristic. Firstly, we prove a Cartier type structure theorem for cocomplete A/k-bialgebras. Secondly, we generalize Michaelis’s theorem. In particular, we prove that a restricted (k, K)-Lie algebra is proper if and only if its restricted enveloping algebra is proper.

Keywords:

• Restricted Lie algebras
• (k, A)-Lie algebras
• A/k-bialgebras
• proper algebras

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B50
• 17B35
• 16T10
• 16T15

Disclosure statement

No potential conflict of interest was reported by the author.