Homotopy Properties of Differential Lie Modules over Curved Coalgebras and Koszul Duality
Matematičeskie zametki, Tome 94 (2013) no. 3, pp. 354-372.

Voir la notice de l'article provenant de la source Math-Net.Ru

The notion of differential Lie module over a curved coalgebra is introduced. The homotopy invariance of the structure of a differential Lie module over a curved coalgebra is proved. A relationship between the homotopy theory of differential Lie modules over curved coalgebras and the theory of Koszul duality for quadratic-scalar algebras over commutative unital rings is determined.
Keywords: differential Lie module over a curved coalgebra, Koszul duality, quadratic-scalar algebra, differential module over a Clifford algebra, differential module over an exterior algebra, SDR-data for differential modules.
Mots-clés : co-$B$-construction
@article{MZM_2013_94_3_a4,
     author = {S. V. Lapin},
     title = {Homotopy {Properties} of {Differential} {Lie} {Modules} over {Curved} {Coalgebras} and {Koszul} {Duality}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {354--372},
     publisher = {mathdoc},
     volume = {94},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a4/}
}
TY  - JOUR
AU  - S. V. Lapin
TI  - Homotopy Properties of Differential Lie Modules over Curved Coalgebras and Koszul Duality
JO  - Matematičeskie zametki
PY  - 2013
SP  - 354
EP  - 372
VL  - 94
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a4/
LA  - ru
ID  - MZM_2013_94_3_a4
ER  - 
%0 Journal Article
%A S. V. Lapin
%T Homotopy Properties of Differential Lie Modules over Curved Coalgebras and Koszul Duality
%J Matematičeskie zametki
%D 2013
%P 354-372
%V 94
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a4/
%G ru
%F MZM_2013_94_3_a4
S. V. Lapin. Homotopy Properties of Differential Lie Modules over Curved Coalgebras and Koszul Duality. Matematičeskie zametki, Tome 94 (2013) no. 3, pp. 354-372. http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a4/

[1] L. E. Positselskii, “Neodnorodnaya kvadratichnaya dvoistvennost i krivizna”, Funkts. analiz i ego pril., 27:3 (1993), 57–66 | MR | Zbl

[2] S. B. Priddy, “Koszul resolutions”, Trans. Amer. Math. Soc., 152 (1970), 39–60 | DOI | MR | Zbl

[3] J. Hirsh, J. Millés, Curved Koszul Duality Theory, arXiv: 1008.5368v1

[4] V. Ginzburg, M. Kapranov, “Koszul duality for operads”, Duke Math. J., 76:1 (1994), 203–272 | DOI | MR | Zbl

[5] V. A. Smirnov, “Algebry Li nad operadami i ikh primenenie v teorii gomotopii”, Izv. RAN. Ser. matem., 62:3 (1998), 121–154 | DOI | MR | Zbl

[6] J. P. May, Simplicial Objects in Algebraic Topology, Van Nostrand Math. Stud., 11, D. Van Nostrand, Princeton, NJ, 1967 | MR | Zbl

[7] V. A. Smirnov, Simplitsialnye i operadnye metody v algebraicheskoi topologii, Faktorial, M., 2002

[8] S. V. Lapin, “Differentsialnye vozmuscheniya i $D_\infty $-differentsialnye moduli”, Matem. sb., 192:11 (2001), 55–76 | DOI | MR | Zbl

[9] S. V. Lapin, “$D_\infty$-differentsialnye $E_\infty$-algebry i spektralnye posledovatelnosti rassloenii”, Matem. sb., 198:10 (2007), 3–30 | DOI | MR | Zbl

[10] S. V. Lapin, “Multiplikativnaya $A_\infty$-struktura v spektralnykh posledovatelnostyakh rassloenii”, Fundament. i prikl. matem., 14:6 (2008), 141–175 | MR