Algebra Seminar: Hochschild (co)homology, global dimension, classical and tau-version

Abstract: We will begin by recalling Hochschild (co)homology and computing the dimensions for radical square zero algebras. We will then move on to the global dimension of finite-dimensional algebras over a field, Happel’s question and Han’s conjecture. Next, we will revisit the Auslander–Reiten duality formula, which we will use to define the tau-Hochschild (co)homology.

We will present properties of this new theory and compute the corresponding dimensions for radical square zero algebras, demonstrating that, in general, these dimensions are strictly greater than those in the classical case.

Then, we will introduce the notion of algebras of infinite + (or co+) global dimension—these are algebras with infinite global dimension. We provide arguments supporting our belief that all such algebras fall into this category. When the Yoneda algebra is infinite-dimensional but finitely generated, this holds—also for local algebras.

If all finite-dimensional algebras of infinite global dimension are indeed of infinite + and co+ global dimension, then the tau-analogues of Happel’s question and Han’s conjecture hold true.

This is joint work with Marcelo Lanzilotta, Eduardo N. Marcos, and Andrea Solotar.

Join on site or via Zoom link (Meeting ID: 645 5572 6999, please contact the organizer for passcode)

This is a seminar in our algebra seminar series.