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A Primer on Twists in the Noncommutative Realm Focusing on Algebra, Representation Theory, and Geometry

Published 29 Nov 2022 in math.RA, math.QA, and math.RT | (2211.15885v3)

Abstract: We review several techniques that twist an algebra's multiplicative structure. We first consider twists by an automorphism, also known as Zhang twists, and we relate them to 2-cocycle twists of certain bialgebras. We then outline the classification and properties of twisted tensor products, and we examine twisted Segre products. Our exposition emphasizes clarity over generality, providing a wealth of interconnecting examples.

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