Derived equivalence of symmetric special biserial algebras

We introduce Brauer complex of symmetric special biserial algebra, and reformulate in terms of Brauer complex the presently known invariants of stable and derived equivalence of symmetric special biserial algebra. 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. As a consequence, symmetric special biserial algebra with Brauer complex of genus 0 are classified.