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Hochschild cohomology of general twisted tensor products

Pablo Ocal (Texas A&M)
Tuesday, November 10, 2020 - 2:30pm
via Zoom
Pablo Ocal

The Hochschild cohomology is a tool for studying associative algebras that has a lot of structure: it is a Gerstenhaber algebra. This structure is useful because of its applications in deformation and representation theory, and recently in quantum symmetries. Unfortunately, computing it remains a notoriously difficult task. In this talk we will present techniques that give explicit formulas of the Gerstenhaber algebra structure for general twisted tensor product algebras. This will include an unpretentious introduction to this cohomology and to our objects of interest, as well as the unexpected generality of the techniques. This is joint work with Tekin Karadag, Dustin McPhate, Tolulope Oke, and Sarah Witherspoon.

The talk will start with a pre-seminar at 2pm:

Title: An overview of Hochschild cohomology
Abstract: Taking Hochschild cohomology is a way of algebraically encoding infinitesimal information about an associative algebra. In this talk we will give an unpretentious introduction to this cohomology, we will justify its importance by computing some of the lower degrees, and we will then give explicit applications that advance the understanding of quantum symmetries.


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