Geodesic
Dihedral modules with $\infty$-simplicial faces and dihedral homology of involutive $A_\infty$-algebras over rings
Algebra i analiz, Tome 33 (2021) no. 3, pp. 85-110.

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S. V. Lapin. Dihedral modules with $\infty$-simplicial faces and dihedral homology of involutive $A_\infty$-algebras over rings. Algebra i analiz, Tome 33 (2021) no. 3, pp. 85-110. http://geodesic.mathdoc.fr/item/AA_2021_33_3_a4/

[1] Tsygan B. L., “O gomologiyakh nekotorykh matrichnykh superalgebr Li”, Funkts. anal. i ego pril., 20:2 (1986), 90–91 | MR | Zbl

[2] Krasauskas R. L., Lapin S. V., Solovev Yu. P., “Diedralnye gomologii i kogomologii. Osnovnye ponyatiya i konstruktsii”, Mat. sb., 133:1 (1987), 25–48 | MR | Zbl

[3] Solovev Yu. P., “Algebraicheskaya $K$-teoriya kvadratichnykh form”, Itogi nauki i tekhn. Ser. Algebra. Topol. Geom., 24, 1986, 121–194 | Zbl

[4] Braun C., Involutive $A_\infty$-algebras and dihedral cohomology, 12 Sep 2013, arXiv: 1209.1261v4 [math.QA] | MR

[5] Karoubi M., “Théorie de Quillen et homologie du groupe orthogonal”, Ann. of Math. (2), 112 (1980), 207–257 | DOI | MR | Zbl

[6] Penkava M., Schwarz A., $A_\infty$-algebras and the cohomology of moduli spaces, 1995, 17 pp., arXiv: hep-th/9408064v2 | MR | Zbl

[7] Lapin S. V., “Gomotopicheskie simplitsialnye grani i gomologii realizatsii simplitsialnykh topologicheskikh prostranstv”, Mat. zametki, 94:5 (2013), 661–681 | Zbl

[8] Lapin S. V., “Differentsialnye moduli Li nad iskrivlennymi krashennymi koalgebrami i $\infty$-simplitsialnye moduli”, Mat. zametki, 96:5 (2014), 709–731 | Zbl

[9] Lapin S. V., “Gomotopicheskie svoistva $\infty$-simplitsialnykh koalgebr i gomotopicheski unitalnye dopolnennye $A_\infty$-algebry”, Mat. zametki, 99:1 (2016), 55–77 | MR | Zbl

[10] Lyubashenko V. V., Homotopy unital $A_\infty$-algebras, 2012, 26 pp., arXiv: 1205.6058v1 [math.KT] | MR

[11] Connes A., “Noncommutative differential geometry”, Inst. Hautes Ètudes Sci. Publ. Math., 62:2 (1985), 257–360 | MR

[12] Tsygan B. L., “Gomologii matrichnykh algebr Li nad koltsami i gomologii Khokhshilda”, Uspekhi mat. nauk, 38:2 (1983), 217–218 | MR | Zbl

[13] Connes A., “Cohomologie cyclique et foncteurs ${\rm Ext}^n$”, C. R. Acad. Sci. Paris Ser. I Math., 296:23 (1983), 953–958 | MR | Zbl

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

[15] Lapin S. V., “Tsiklicheskie moduli s $\infty$-simplitsialnymi granyami i tsiklicheskie gomologii $A_\infty$-algebr”, Mat. zametki, 102:6 (2017), 874–895 | Zbl

[16] Stasheff J. D., “Homotopy associativity of $H$-spaces I, II”, Trans. Amer. Math. Soc., 108:2 (1963), 275–312 | MR | Zbl

[17] Kadeishvili T. V., “K teorii gomologii rassloennykh prostranstv”, Uspekhi mat. nauk, 35 (1980), 183–188 | MR | Zbl

[18] Loday J.-L., Vallette B., Algebraic operads, Grundlehren Math. Wiss., 346, Springer-Verlag, Berlin, 2012 | DOI | MR | Zbl