REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: Suppose R is a k-algebra, and let P be resolution of R by projective bimodules. Then P is idempotent, in the sense that P tensor P is homotopy equivalent to P. In this talk I will discuss these and other "categorical idempotents". The main goal will be to introduce a down-to-earth construction of categorical idempotents which is reminiscent of the bar construction. Depending on time and interest we might also discuss generalizations of Hochschild and group cohomology that come out of this story, and the natural Lie bracket with which they are equipped.