Compact coalgebras, compact quantum groups and the positive antipode

  • Andrés Abella Universidad de la República Facultad de Ciencias
  • Walter Ferrer Santos Universidad de la República Facultad de Ciencias
  • Mariana Haim Universidad de la República Facultad de Ciencias

Resumo

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 Nakayama automorphism– in order to enhance our understanding of the antipode itself.

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Publicado
2009-12-30
Como Citar
Abella, A., Santos, W., & Haim, M. (2009). Compact coalgebras, compact quantum groups and the positive antipode. São Paulo Journal of Mathematical Sciences, 3(2), 193-229. https://doi.org/10.11606/issn.2316-9028.v3i2p193-229
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Artigos