Derivations and invariant forms of Jordan and alternative tori

Neher, Erhard; Yoshii, Yoji

doi:10.1090/S0002-9947-02-03013-1

Derivations and invariant forms of Jordan and alternative tori
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by Erhard Neher and Yoji Yoshii

Trans. Amer. Math. Soc. 355 (2003), 1079-1108

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

Published electronically: November 1, 2002

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Abstract:

Jordan and alternative tori are the coordinate algebras of extended affine Lie algebras of types $\mathrm {A}_1$ and $\mathrm {A}_2$. 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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