Cyclic complexes, Hall polynomials and simple Lie algebras

Autor: Qinghua Chen, Bangming Deng
Rok vydání: 2015
Předmět:
Zdroj: Journal of Algebra. 440:1-32
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2015.04.043
Popis: In this paper we study the category C m ( P ) of m -cyclic complexes over P , where P is the category of projective modules over a finite dimensional hereditary algebra A , and describe almost split sequences in C m ( P ) . This is applied to prove the existence of Hall polynomials in C m ( P ) when A is representation finite and m ≠ 1 . We further introduce the Hall algebra of C m ( P ) and its localization in the sense of Bridgeland. In the case when A is representation finite, we use Hall polynomials to define the generic Bridgeland–Hall algebra of A and show that it contains a subalgebra isomorphic to the integral form of the corresponding quantum enveloping algebra. This provides a construction of the simple Lie algebra associated with A .
Databáze: OpenAIRE
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