Derived equivalence of symmetric special biserial algebras

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We introduce Brauer complex of symmetric SB-algebra, and reformulate in terms of Brauer complex the so far known invariants of stable and derived equivalence of symmetric SB-algebras. In particular, the genus of Brauer complex turns out to be invariant under derived equivalence. We study transformations of Brauer complexes which preserve class of derived equivalence. Additionally, we establish a new invariant of derived equivalence of symmetric SB-algebras. As a consequence, symmetric SB-algebras with Brauer complex of genus 0 are classified. Keywords: Brauer tree algebras, special biserial algebras, tilting complex.
19 pages, 13 figures

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Representation Theory, Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/122415

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0701586
 http://arxiv.org/abs/math/0701586

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arXiv