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Cohomological properties of the quantum shuffle product and application to the construction of quasi-Hopf algebras

Cyrille Ospel
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Abstract

For a commutative algebra the shuffle product is a morphism of complexes. We generalize this result to the quantum shuffle product, associated to a class of non-commutative algebras (for example all the Hopf algebras). As a first application we show that the Hochschild-Serre identity is the dual statement of our result. In particular, we extend this identity to Hopf algebras. Secondly, we clarify the construction of a class of quasi-Hopf algebras.

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BibTeXRIS

Cyrille Ospel. 2001-12-13. Cohomological properties of the quantum shuffle product and application to the construction of quasi-Hopf algebras. https://arxiv.org/abs/math/0112141

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