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arXiv · 1411.3734

Isomorphism invariants of enveloping algebras

Hamid Usefi
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Abstract

Let $L$ be a Lie algebra with its enveloping algebra $U(L)$ over a field. In this paper we survey results concerning the isomorphism problem for enveloping algebras: given another Lie algebra $H$ for which $U(L)$ and $U(H)$ are isomorphic as associative algebras, can we deduce that $L$ and $H$ are isomorphic Lie algebras? Over a field of positive characteristic we consider a similar problem for restricted Lie algebras, that is, given restricted Lie algebras $L$ and $H$ for which their restricted enveloping algebras are isomorphic as algebras, can we deduce that $L$ and $H$ are isomorphic?

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Hamid Usefi. 2014-11-13. Isomorphism invariants of enveloping algebras. https://arxiv.org/abs/1411.3734

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