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Covering Algebras I. Extended Affine Lie Algebras

✍ Scribed by Bruce Allison; Stephen Berman; Arturo Pianzola

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
231 KB
Volume
250
Category
Article
ISSN
0021-8693

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✦ Synopsis

This is the first of what will be a sequence of three papers dealing with a generalization of certain parts of the beautiful work of V. Kac on finiteorder automorphisms of finite-dimensional complex simple Lie algebras. Recall that Kac (see [K2, Chap. 8] and [H, Sect. X.5]) built a Lie algebra from a pair ( σ) composed of a finite-order automorphism σ of a finitedimensional simple Lie algebra over as follows. First from σ he obtains the eigenspaces ī = x ∈ σ x = ζ i x where m is on the order of σ, ζ = e 2πi √ -1/m i ∈ , and i → ī is the natural map of → m (here m denotes the integers modulo m). He 1 The authors gratefully acknowledge the support of the Natural Sciences and Engineering Research Council of Canada.

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