Semisimple weak Hopf algebras

Details Semisimple weak Hopf algebras Semisimple weak Hopf algebras

2003-04-07

arxiv.org/abs/math/0304098v3

J. Algebra 275 (2004), 639 - 667.

Mathematics

Quantum Algebra

Ams-latex, 24 pages, an error in Proposition 3.4.2 is corrected

Scientific paper

We develop the theory of semisimple weak Hopf algebras and obtain analogues of a number of classical results for ordinary semisimple Hopf algebras. We prove a criterion for semisimplicity and analyze the square of the antipode S^2 of a semisimple weak Hopf algebra A. We explain how the Frobenius-Perron dimensions of irreducible A-modules and eigenvalues of S^2 can be computed using the inclusion matrix associated to A. A trace formula of Larson and Radford is extended to a relation between the global and Frobenius-Perron dimensions of A. Finally, an analogue of the Class Equation of Kac and Zhu is established and properties of $A$-module algebras and their dimensions are studied.

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