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arXiv · 1202.2103

Analytic Free Semigroup Algebras and Hopf Algebras

Dilian Yang
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Abstract

Let $\fS$ be an analytic free semigroup algebra. In this paper, we explore richer structures of $\fS$ and its predual $\fS_*$. We prove that $\fS$ and $\fS_*$ both are Hopf algebras. Moreover, the structures of $\fS$ and $\fS_*$ are closely connected with each other: There is a bijection between the set of completely bounded representations of $\fS_*$ and the set of corepresentations of $\fS$ on one hand, and $\fS$ can be recovered from the coefficient operators of completely bounded representations of $\fS_*$ on the other hand. As an amusing application of our results, the (Gelfand) spectrum of $\fS_*$ is identified. Surprisingly, the main results of this paper seem new even in the classical case.

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Dilian Yang. 2012-02-09. Analytic Free Semigroup Algebras and Hopf Algebras. https://arxiv.org/abs/1202.2103

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