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Structurable tori and extended affine Lie algebras of type BC1

✍ Scribed by Bruce Allison; Yoji Yoshii

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
368 KB
Volume
184
Category
Article
ISSN
0022-4049

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✦ Synopsis

Structurable n-tori are nonassociative algebras with involution that generalize the quantum n-tori with involution that occur as coordinate structures of extended a ne Lie algebras. We show that the core of an extended a ne Lie algebra of type BC1 and nullity n is a central extension of the Kantor Lie algebra obtained from a structurable n-torus over C. With this result as motivation, we prove general properties of structurable n-tori and show that they divide naturally into three classes. We classify tori in one of the three classes in general, and we classify tori in the other classes when n = 2. It turns out that all structurable 2-tori are obtained from hermitian forms over quantum 2-tori with involution.

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