✦ LIBER ✦

Composition Algebras of Affine Type

✍ Scribed by Pu Zhang

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 394 KB
Volume: 206
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7447

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✦ Synopsis

The aim of this paper is to study the structure of the composition algebras of affine type. It turns out that they have a triangular decomposition P P m T T m I I corresponding to the division of the indecomposables into the preprojectives, the regulars, and the preinjectives. By the recent Ringel᎐Green theorem the composition algebra can be twisted in order to obtain the positive part U q of the Drinfeld᎐Jimbo quantized enveloping algebra U s U y m U 0 m U q of the corresponding Kac᎐Moody algebra, and one obtains a corresponding triangular decomposition for U q , in particular, a natural basis of U q in terms of A-representations.

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