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Pré-Publication, Document De Travail Année : 2012

Homologies of Algebraic Structures via Braidings and Quantum Shuffles

Résumé

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.
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Dates et versions

hal-00687866 , version 1 (15-04-2012)
hal-00687866 , version 2 (27-10-2012)

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Victoria Lebed. Homologies of Algebraic Structures via Braidings and Quantum Shuffles. 2012. ⟨hal-00687866v2⟩
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