Dual coalgebras of twisted tensor products

Abstract

We investigate cases where the finite dual coalgebra of a twisted tensor product of two algebras is a cotwisted tensor product of their respective finite dual coalgebras. This is achieved by interpreting the finite dual as a topological dual; in order to prove this, we show that the continuous dual is a strong monoidal functor on linearly topologized vector spaces whose open subspaces have finite codimension. We describe a sufficient condition for the result on finite dual coalgebras to be applied, and we this condition to particular constructions including Ore extensions, smash product algebras, and crossed product bialgebras.

30 pages. Section 5 added with several new examples. This paper includes material that was removed from an earlier version of arXiv:2111.07081

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