Isomorphism invariants of restricted enveloping algebras

Details Isomorphism invariants of restricted enveloping algebras Isomorphism invariants of restricted enveloping algebras

2008-04-14

arxiv.org/abs/0804.2281v3

Mathematics

Rings and Algebras

Pacific Journal of Mathematics, to appear

Scientific paper

Let $L$ and $H$ be finite-dimensional restricted Lie algebras over a perfect field $\F$ such that $u(L)\cong u(H)$, where $u(L)$ is the restricted enveloping algebra of $L$. We prove that if $L$ is $p$-nilpotent and abelian, then $L\cong H$. We deduce that if $L$ is abelian and $\F$ is algebraically closed, then $L\cong H$. We use these results to prove the main result of this paper stating that if $L$ is $p$-nilpotent, then $L/L'^p+\gamma_3(L)\cong H/H'^p+\gamma_3(H)$.

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