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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The restricted isomorphism problem for metacyclic restricted Lie algebras


Author: Hamid Usefi
Journal: Proc. Amer. Math. Soc. 136 (2008), 4125-4133
MSC (2000): Primary 17B35, 17B50; Secondary 20C05
Published electronically: July 23, 2008
MathSciNet review: 2431023
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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.


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Additional Information

Hamid Usefi
Affiliation: Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, Canada, V6T 1Z2
Email: usefi@math.ubc.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09632-9
PII: S 0002-9939(08)09632-9
Keywords: Restricted Lie algebras, metacylic, enveloping algebras, isomorphism problem, modular group algebras
Received by editor(s): September 28, 2007
Published electronically: July 23, 2008
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2008 American Mathematical Society