REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: In any monoidal category one can consider the notion of an (algebra or) coalgebra object. If the comultiplication map C → C ⊗ C happens to be an isomorphism, then our coalgebra is said to be idempotent. For example the two-sided bar complex of an algebra A is an idempotent coalgebra in the homotopy category of complexes of (A,A)-bimodules. In this talk I will explain how the notion of coalgebras which are "idempotent up to homotopy" is responsible for the Gerstenhaber Lie bracket on the algebra Hom(C, 1). This explains and generalizes the usual Gerstenhaber bracket on Hochschild cohomology of an algebra.