Andrea Solotar, University of Buenos Aires and Guangdong Technion-Israel Institute of Technology

Title: On the tau-tilting Hochschild (co)homology of an algebra

Abstract: In this talk I will introduce the tau-tilting Hochschild cohomology and homology of a finite dimensional k-algebra A, where k is a field, with coefficients in an A-bimodule X. I will compute the dimension of the n-th tau-tilting Hochschild cohomology for all n. The result is expressed as an alternating sum of the dimensions of classical Hochschild cohomology in lower degrees, plus an alternating sum of the dimensions of vector spaces taking into account the Ext-algebra of A as well as the Peirce decomposition of the bimodule X. I will also formulate a tau-tilting analogue of a question by Happel and of Han’s conjecture. This is a joint work with Claude Cibils, Marcelo Lanzilotta and Eduardo Marcos.