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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a restricted Lie algebra with the restricted enveloping algebra over a perfect field of positive characteristic . The restricted isomorphism problem asks what invariants of are determined by . This problem is the analogue of the modular isomorphism problem for finite -groups. Bagiński and Sandling have given a positive answer to the modular isomorphism problem for metacyclic -groups. In this paper, we provide a positive answer to the restricted isomorphism problem in case is metacyclic and -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:
https://doi.org/10.1090/S0002-9939-08-09632-9

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