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Differential Lie modules over curved colored coalgebras and ∞-simplicial modules

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Abstract

The notion of differential Lie module over a curved colored coalgebra is introduced. The homotopy invariance of the structure of differential Lie module over a curved colored coalgebra is proved. The notion of ∞-simplicial module is introduced using the construction of a differential Lie module over a curved colored coalgebra and the Koszul duality theory for quadratic-scalar colored algebras. The homotopy invariance of the structure of a ∞-simplicial module is proved.

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  1. Matematicheskie Zametki, Steklov Mathematical Institute, Moscow, Russia

    S. V. Lapin

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  1. S. V. Lapin
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Correspondence to S. V. Lapin.

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Original Russian Text © S. V. Lapin, 2014, published in Matematicheskie Zametki, 2014, Vol. 96, No. 5, pp. 709–731.

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Lapin, S.V. Differential Lie modules over curved colored coalgebras and ∞-simplicial modules. Math Notes 96, 698–715 (2014). https://doi.org/10.1134/S0001434614110091

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