Integral theory for Hopf (co)quasigroups

Details Integral theory for Hopf (co)quasigroups Integral theory for Hopf (co)quasigroups

2010-04-22

arxiv.org/abs/1004.3929v2

Mathematics

Quantum Algebra

18 pages latex no figures

Scientific paper

We recall the notion of a Hopf (co)quasigroup defined in \cite{Kl09} and define integration and Fourier Transforms on these objects analogous to those in the theory of Hopf algebras. Using the general Hopf module theory for Hopf (co)quasigroups from \cite{Br09} we show that a finite dimensional Hopf (co)quasigroup has a unique integration up to scale and an invertible antipode. We also supply the inverse Fourier transformation and show that it maps the convolution product on $H$ to the product in its dual $H^*$. Finally, we further develop the theory to consider Frobenius Hopf (co)quasigroups, separability and semisimplicity.

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