The restricted isomorphism problem for metacyclic restricted Lie algebras

Usefi, Hamid

doi:10.1090/S0002-9939-08-09632-9

The restricted isomorphism problem for metacyclic restricted Lie algebras
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Proc. Amer. Math. Soc. 136 (2008), 4125-4133 Request permission

Abstract:

Let $L$ be a restricted Lie algebra with the restricted enveloping algebra $u(L)$ over a perfect field of positive characteristic $p$. The restricted isomorphism problem asks what invariants of $L$ are determined by $u(L)$. This problem is the analogue of the modular isomorphism problem for finite $p$-groups. Bagiński and Sandling have given a positive answer to the modular isomorphism problem for metacyclic $p$-groups. In this paper, we provide a positive answer to the restricted isomorphism problem in case $L$ is metacyclic and $p$-nilpotent.

References

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