On integrals and cointegrals for quasi-Hopf algebras

Details On integrals and cointegrals for quasi-Hopf algebras On integrals and cointegrals for quasi-Hopf algebras

2011-03-11

arxiv.org/abs/1103.2263v2

Mathematics

Quantum Algebra

29 pages, to appear in J. Algebra

Scientific paper

Using the machinery provided by a Frobenius algebra we show how the antipode of a quasi-Hopf algebra $H$ carries out left or right cointegrals for $H$. These formulas will allow us to find out the explicit form of an integral and a cointegral for the quantum double $D(H)$ of $H$ in terms of those of $H$, and so to answer to a conjecture of Hausser and Nill raised at the end of the nineties.

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