  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.
