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

 

Lie superautomorphisms on associative algebras


Authors: Yuri Bahturin and Matej Bresar
Journal: Proc. Amer. Math. Soc. 138 (2010), 417-425
MSC (2000): Primary 17B40; Secondary 16W10, 16R50, 17B60
Published electronically: October 1, 2009
MathSciNet review: 2557159
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Abstract: The results on Lie homomorphisms of associative algebras are extended to certain associative superalgebras. It is shown that under appropriate conditions a Lie superautomorphism of $ A=A_0\oplus A_1$ is a sum of a superautomorphism or the negative of a superantiautomorphism and a central map. In particular we consider the situation when $ A$ is a central simple algebra and its $ \mathbb{Z}_2$-grading is induced by an idempotent.


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Additional Information

Yuri Bahturin
Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, A1C5S7, Canada
Email: yuri@math.mun.ca

Matej Bresar
Affiliation: Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, Ljubljana, Slovenia – and – Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, Maribor, Slovenia
Email: matej.bresar@fmf.uni-lj.si

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10136-3
PII: S 0002-9939(09)10136-3
Received by editor(s): March 30, 2009
Published electronically: October 1, 2009
Additional Notes: The first author was partially supported by NSERC grant #227060-04 and URP grant, Memorial University of Newfoundland.
The second author was partially supported by ARRS grant #P1-0288.
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2009 American Mathematical Society