Geodesic
Braided systems: a unified treatment of algebraic structures with several operations
Homology, homotopy, and applications, Tome 19 (2017) no. 2, pp. 141-174.

Voir la notice de l'article provenant de la source International Press of Boston

Bialgebras and Hopf (bi)modules are typical algebraic structures with several interacting operations. Their structural and homological study is therefore quite involved. We develop the machinery of braided systems, tailored for handling such multi-operation situations. Our construction covers the above examples (as well as Poisson algebras, Yetter–Drinfel’d modules, and several other structures, treated in separate publications). In spite of this generality, graphical tools allow an efficient study of braided systems, in particular, of their representation and homology theories. These latter naturally recover, generalize, and unify standard homology theories for bialgebras and Hopf (bi)modules (due to Gerstenhaber–Schack, Panaite–Ştefan, Ospel, Taillefer); and the algebras encoding their representation theories (Heisenberg double, algebras $\mathscr{X}, \mathscr{Y}, \mathscr{Z}$ of Cibils–Rosso and Panaite). Our approach yields simplified and conceptual proofs of the properties of these objects.
DOI : 10.4310/HHA.2017.v19.n2.a9
Classification : 16E40, 16T05, 16T10, 16T25, 18D10
Keywords: braided system, braided homology, Hopf algebra, Hopf (bi)module, Heisenberg double, crossed product, bialgebra homology, distributive law, multi-quantum shuffle algebra 
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     author = {Victoria Lebed},
     title = {Braided systems: a unified treatment of algebraic structures with several operations},
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     pages = {141--174},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2017.v19.n2.a9/}
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Victoria Lebed. Braided systems: a unified treatment of algebraic structures with several operations. Homology, homotopy, and applications, Tome 19 (2017) no. 2, pp. 141-174. doi : 10.4310/HHA.2017.v19.n2.a9. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2017.v19.n2.a9/

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