Algebraic quantum hypergroups

  title={Algebraic quantum hypergroups},
  author={Lydia Delvaux and Alfons Van Daele},
Abstract An algebraic quantum group is a regular multiplier Hopf algebra with integrals. In this paper we will develop a theory of algebraic quantum hypergroups . It is very similar to the theory of algebraic quantum groups, except that the comultiplication is no longer assumed to be a homomorphism. We still require the existence of a left and of a right integral. There is also an antipode but it is characterized in terms of these integrals. We construct the dual, just as in the case of… CONTINUE READING


Publications referenced by this paper.

Van Daele : Compact and discrete subgroups of algebraic quantum groups

M. B. Lanstad, A.
  • 2006

Van Daele : Multiplier Hopf ∗algebras and groups with compact open subgroups

  • 2006

Woronowicz : Compact matrix pseudogroups

L. S.
  • J . of Alg .
  • 2006

Zhang : A survey on multiplier Hopf algebras . Proceedings of the conference in Brussels on Hopf Algebras and Quantum Groups

A. Van Daele, Y.
  • Preprint K . U . Leuven
  • 2006

Kustermans : The analytic structure of algebraic quantum groups

J. Ku
  • J . of Alg .
  • 2003

Vaes : Locally compact quantum groups in the von Neumann algebra setting

J. Kustermans, S.
  • Math . Scand .
  • 2003

Van Daele : Locally compact quantum groups . A von Neumann algebra approach

  • Vainerman . Walter de Gruyter
  • 2003

Van Daele : Multiplier Hopf ∗algebras with positive integrals : A laboratory for locally compact quantum groups

Ed. V. Turaev, L.
  • Irma Lectures in Mathematical and Theoretical Physics 2 : Locally compact Quantum Groups and Groupoids . Proceedings of the meeting in Strasbourg on Hopf algebras , quantum groups and their applications
  • 2002

Kalyuzhnyi : Conditional expectations on quantum groups and new examples of quantum hypergroups

A. KaA.
  • Methods of Funct . Anal . Topol .
  • 2001

Vaes : Locally compact quantum groups

J. Kustermans, S.
  • Ann . Sci . Éc . Norm . Sup .
  • 2000