# Weak Hopf Algebras: I. Integral Theory and C-Structure

@article{Bhm1998WeakHA, title={Weak Hopf Algebras: I. Integral Theory and C-Structure}, author={Gabriella B{\`o}hm and Florian Nill and Korn{\'e}l Szlach{\'a}nyi}, journal={Journal of Algebra}, year={1998}, volume={221}, pages={385-438} }

We give an introduction to the theory of weak Hopf algebras proposed 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 AL and AR 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…

## 459 Citations

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Abstract If A is a weak C *-Hopf algebra then the category of finite-dimensional unitary representations of A is a monoidal C *-category with its monoidal unit being the GNS representation D e…

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