Dual coalgebras as a quantized maximal spectrum

Abstract: If an algebra A has “many” finite-dimensional representations, we argue that its Sweedler dual coalgebra is a reasonable functorial quantization of the maximal spectrum of A. Many such algebras arise as twisted tensor products of commutative algebras, including Ore extensions and smash products. This leads to the problem of understanding the dual coalgebra of a twisted tensor product. We will discuss when the Sweedler dual of a twisted tensor product can be computed as a cross product coalgebra, a result that is achieved using methods of topological algebra.

rings and algebrasrepresentation theory

Audience: researchers in the topic

ONCAS Online Noncommutative Algebra Seminar

Series comments: This is an online seminar organized to keep the community of noncommutative algebraists connected during the pandemic which has made it difficult for everyone to travel. If you would like to attend these talks, please email to any of the organizers and you will be added to the mailing list.