Compact coalgebras, compact quantum groups and the positive antipode
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.
Keywords
Cite
@article{arxiv.0907.1183,
title = {Compact coalgebras, compact quantum groups and the positive antipode},
author = {A. Abella and W. Ferrer Santos and M. Haim},
journal= {arXiv preprint arXiv:0907.1183},
year = {2009}
}