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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Derivations and invariant forms of Jordan and alternative tori


Authors: Erhard Neher and Yoji Yoshii
Journal: Trans. Amer. Math. Soc. 355 (2003), 1079-1108
MSC (2000): Primary 17C10; Secondary 17B60, 17B70, 17C60
Published electronically: November 1, 2002
MathSciNet review: 1938747
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Abstract: Jordan and alternative tori are the coordinate algebras of extended affine Lie algebras of types ${A}_1$ and ${A}_2$. In this paper we show that the derivation algebra of a Jordan torus is a semidirect product of the ideal of inner derivations and the subalgebra of central derivations. In the course of proving this result, we investigate derivations of the more general class of division graded Jordan and alternative algebras. We also describe invariant forms of these algebras.


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Additional Information

Erhard Neher
Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
Email: neher@uottawa.ca

Yoji Yoshii
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Address at time of publication: Department of Mathematics, Van Vleck Hall, University of Wisconsin-Madison, Madison, Wisconsin 53706
Email: yoshii@math.ualberta.ca, yoshii@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03013-1
PII: S 0002-9947(02)03013-1
Received by editor(s): April 3, 2001
Received by editor(s) in revised form: January 31, 2002
Published electronically: November 1, 2002
Additional Notes: The research of the first author was partially supported by an NSERC (Canada) research grant
The research of the second author was supported by a Fields Postdoctoral Fellowship (Fall 2000) and a PIMS Postdoctoral Fellowship (2001)
Dedicated: Dedicated to Holger Petersson
Article copyright: © Copyright 2002 American Mathematical Society