Homologies of Algebraic Structures via Braidings and Quantum ShufflesReport as inadecuate




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* Corresponding author 1 IMJ - Institut de Mathématiques de Jussieu

Abstract : In this paper we construct -structural- pre-braidings characterizing different algebraic structures: a rack, an associative algebra, a Leibniz algebra and their representations. Some of these pre-braidings seem original. On the other hand, we propose a general homology theory for pre-braided vector spaces and braided modules, based on the quantum co-shuffle comultiplication. Applied to the structural pre-braidings above, it gives a generalization and a unification of many known homology theories. All the constructions are categorified, resulting in particular in their super- and co-versions. Loday-s hyper-boundaries, as well as certain homology operations are efficiently treated using the -shuffle- tools.

Keywords : pre-braiding braided coalgebra braided homology character braided module quantum shuffle algebra Koszul complex rack homology Hochschild homology Leibniz algebra pre-braided object





Author: Victoria Lebed -

Source: https://hal.archives-ouvertes.fr/



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