Weak Hopf Algebras I: Integral Theory and C^*-structure

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dc.creatorBohm, G.
dc.creatorNill, F.
dc.creatorSzlachanyi, K.
dc.date1998-05-26
dc.date1999-06-08
dc.date.accessioned2026-07-07T05:24:51Z
dc.date.available2026-07-07T05:24:51Z
dc.descriptionWe give an introduction to the theory of weak Hopf algebras proposed recently as a coassociative alternative of weak quasi-Hopf algebras. We follow an axiomatic approach keeping as close as possible to the "classical" theory of Hopf algebras. The emphasis is put on the new structure related to the presence of canonical subalgebras A^L and A^R in any weak Hopf algebra A that play the role of non-commutative numbers in many respects. A theory of integrals is developed in which we show how the algebraic properties of A, such as the Frobenius property, or semisimplicity, or innerness of the square of the antipode, are related to the existence of non-degenerate, normalized, or Haar integrals. In case of C^*-weak Hopf algebras we prove the existence of a unique Haar measure h in A and of a canonical grouplike element g in A implementing the square of the antipode and factorizing into left and right algebra elements. Further discussion of the C^*-case will be presented in Part II.
dc.description40 pages, LaTeX, to appear in J. Algebra
dc.identifierhttps://arxiv.org/abs/math/9805116
dc.identifierhttp://arxiv.org/abs/math/9805116
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76964
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.titleWeak Hopf Algebras I: Integral Theory and C^*-structure
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