Compact coalgebras, compact quantum groups and the positive antipode

A. Abella; W. Ferrer Santos; M. Haim

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arXiv · 0907.1183

Compact coalgebras, compact quantum groups and the positive antipode

A. Abella·W. Ferrer Santos·M. Haim

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Abstract

In this article -that has also the intention to survey some known results in the theory of compact quantum groups using methods different from the standard and with a strong algebraic flavor- we consider compact o-coalgebras and Hopf algebras. In the case of a o-Hopf algebra we present a proof of the characterization of the compactness in terms of the existence of a positive definite integral, and use our methods to give an elementary proof of the uniqueness - up to conjugation by an automorphism of Hopf algebras- of the compact involution appearing in [4]. We study the basic properties of the positive square root of the antipode square that is a Hopf algebra automorphism that we call the positive antipode. We use it -as well as the unitary antipode and the Nakayama automorphism- in order to enhance our understanding of the antipode itself.

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BibTeX RIS

A. Abella, W. Ferrer Santos, M. Haim. 2009-07-07. Compact coalgebras, compact quantum groups and the positive antipode. https://arxiv.org/abs/0907.1183

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