Analytic free semigroup algebras and Hopf algebras (Q2834133)

A free semigroup algebra is the unital {\textsc{WOT}}-closed (non-selfadjoint) operator algebra generated by an isometric tuple. The prototypical example of free semigroup algebras is the non-commutative analytic Toeplitz algebra \(\mathcal{L}_n\) generated by the left regular representation of the free semigroup with \(n\) generators.NEWLINENEWLINEThe main purpose of this paper is to explore richer structures of an analytic free semigroup algebra generated by an isometric \(n\)-tuple and its (unique) predual. The main results of the paper are that both the analytic free semigroup algebra and its predual are Hopf algebras. This shows a certain analogy between the predual of \(\mathcal{L}_n\) and the Fourier algebra of the free semigroup with \(n\) generators.