Brauer tree algebras and derived equivalence

Self-equivalences of the Derived Category of Brauer Tree Algebras with Exceptional Vertex

Let k be a field and A be a Brauer tree algebra associated with a Brauer tree with possibly non trivial exceptional vertex. In an earlier joint paper with Raphaël Rouquier we studied and defined the group TrP ick(Λ) of standard self-equivalences of the derived category of a kalgebra Λ. In the present note we shall determine a non trivial homomorphism of a group slightly bigger than the pure bra...

Brauer Algebras and the Brauer Group

An algebra is a vector space V over a field k together with a kbilinear product of vectors under which V is a ring. A certain class of algebras, called Brauer algebras algebras which split over a finite Galois extension appear in many subfields of abstract algebra, including K-theory and class field theory. Beginning with a definition of the the tensor product, we define and study Brauer algebr...

Derived and Stable Equivalence Classification of Twisted Multifold Extensions of Piecewise Hereditary Algebras of Tree Type

Derived equivalence of symmetric special biserial algebras

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 ...

Discriminants of Brauer Algebras

In this paper, we compute Gram determinants associated to all cell modules of Brauer algebras Bn(δ). Theoretically, we know when a cell module of Bn(δ) is equal to its simple head. This gives a solution of this long standing problem. On the occasion of Professor Gus Lehrer’s 60 birthday