Description of the cohomology of Banach algebras and locally convex algebras in the language of $A_\infty$-structures
Izvestiya. Mathematics, Tome 62 (1998) no. 4, pp. 789-805
Cet article a éte moissonné depuis la source Math-Net.Ru
We consider the following problem: how can one apply the methods employed for describing the cohomology of algebras and based on the use of the $A_\infty$-structures of Stasheff to describe the cohomology of Banach algebras and locally convex algebras.
@article{IM2_1998_62_4_a5,
author = {V. A. Smirnov and S. V. Kuznetsova and I. V. Mayorova},
title = {Description of the cohomology of {Banach} algebras and locally convex algebras in the language of $A_\infty$-structures},
journal = {Izvestiya. Mathematics},
pages = {789--805},
year = {1998},
volume = {62},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1998_62_4_a5/}
}
TY - JOUR AU - V. A. Smirnov AU - S. V. Kuznetsova AU - I. V. Mayorova TI - Description of the cohomology of Banach algebras and locally convex algebras in the language of $A_\infty$-structures JO - Izvestiya. Mathematics PY - 1998 SP - 789 EP - 805 VL - 62 IS - 4 UR - http://geodesic.mathdoc.fr/item/IM2_1998_62_4_a5/ LA - en ID - IM2_1998_62_4_a5 ER -
%0 Journal Article %A V. A. Smirnov %A S. V. Kuznetsova %A I. V. Mayorova %T Description of the cohomology of Banach algebras and locally convex algebras in the language of $A_\infty$-structures %J Izvestiya. Mathematics %D 1998 %P 789-805 %V 62 %N 4 %U http://geodesic.mathdoc.fr/item/IM2_1998_62_4_a5/ %G en %F IM2_1998_62_4_a5
V. A. Smirnov; S. V. Kuznetsova; I. V. Mayorova. Description of the cohomology of Banach algebras and locally convex algebras in the language of $A_\infty$-structures. Izvestiya. Mathematics, Tome 62 (1998) no. 4, pp. 789-805. http://geodesic.mathdoc.fr/item/IM2_1998_62_4_a5/
[1] Gugenheim V. K., May J. P., “On the theory and applications of differential torsion products”, Mem. AMS, 142 (1974), 1–93 | MR
[2] Stasheff J. D., “Homotopy associativity of $H$-spaces”, Trans. Amer. Math. Soc., 108:2 (1963), 275–312 | DOI | MR | Zbl
[3] Smirnov V. A., “Gomologii $B$-konstruktsii i ko-$B$-konstruktsii”, Izv. RAN. Ser. matem., 58:4 (1994), 80–96 | MR | Zbl
[4] Khelemskii A. Ya., Banakhovy i polinormirovannye algebry, Nauka, M., 1989 | MR