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A Characterization of Certain Loop Lie Algebras

✍ Scribed by J.Marshall Osborn; Kaiming Zhao

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
113 KB
Volume
221
Category
Article
ISSN
0021-8693

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✦ Synopsis

In this paper, we study Z Γ— Z-graded Lie algebras A = i j∈Z A i j with dim A i j ≀ 1 satisfying (I) dim A Β±1 0 = dim A 0 Β±1 = 1, and A is generated by A Β±1 0 A 0 Β±1 ;

(II) i∈Z A 0 j sl 2 ; (III)

A -1 0 A 1 0 = 0, and adA ±1 0 act faithfully on j∈Z A j 1 .

We show that A is necessarily isomorphic to one of the two smallest loop algebras F t t -1 βŠ— sl 2 and ŝl 2 3 with appropriate grading.

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