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

DOI:
https://doi.org/10.1090/S0002-9947-02-03013-1

Published electronically:
November 1, 2002

MathSciNet review:
1938747

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Abstract | References | Similar Articles | Additional Information

Abstract: Jordan and alternative tori are the coordinate algebras of extended affine Lie algebras of types and . 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:
https://doi.org/10.1090/S0002-9947-02-03013-1

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