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.
This publication is cited in the following 8 articles:
Lapin V S., “Homotopy Invariance of the Cyclic Homology of a(Infinity)-Algebras Under Homotopy Equivalences of a(Infinity)-Algebras”, Georgian Math. J., 28:6 (2021), 895–916
S. V. Lapin, “Dihedral modules with ∞-simplicial faces and dihedral homology of involutive A∞-algebras over rings”, St. Petersburg Math. J., 33:3 (2022), 491–509
S. V. Lapin, “Homotopy invariance of dihedral homology of involutive A∞-algebras”, St. Petersburg Math. J., 33:6 (2022), 949–969
S. V. Lapin, “Dihedral infinity-simplicial modules and dihedral homology of involutive homotopy unital a(infinity)-algebras”, Georgian Math. J., 26:2 (2019), 257–286
S. V. Lapin, “Cyclic homology of cyclic infinity-simplicial modules”, Georgian Math. J., 25:4 (2018), 571–591
S. V. Lapin, “Cyclic Modules with ∞-Simplicial Faces and the Cyclic Homology of A∞-Algebras”, Math. Notes, 102:6 (2017), 806–823
S. V. Lapin, “Homotopy Properties of ∞-Simplicial Coalgebras and Homotopy Unital Supplemented A∞-Algebras”, Math. Notes, 99:1 (2016), 63–81
S. V. Lapin, “Chain Realization of Differential Modules with ∞-Simplicial Faces and the B-Construction over A∞-Algebras”, Math. Notes, 98:1 (2015), 111–129
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