✦ LIBER ✦

Triangular Decomposition of Tame Non-Simply Laced Composition Algebras

✍ Scribed by Shunhua Zhang

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 214 KB
Volume: 241
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8770

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✦ Synopsis

the composition algebra of A. Let P P resp. I I be the subalgebra of Ž . Ž . C C A generated by the preprojective resp. preinjective A-modules, and let T T be w x Ž . w x the subalgebra generated by r , where r s Ý M g H H A , M runs over the d d Ž . isomorphism classes of the regular A-modules with dimension vector d, and H H A Ž . is the Ringel᎐Hall algebra of A.

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Let A be a finite-dimensional hereditary algebra over a finite field, and let Ž . Ž . H H A and C C A be, respectively, the Ringel᎐Hall algebra and the composition w x Ž . w x algebra of A. Define r to be the element Ý M g H H A , where M runs over d the isomorphism classes of the regular A-modules