Geodesic
Cocycles in the relative Hochschild cohomology
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 29-35 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Let $E$ be a long exact sequence of modules over an algebra $A$ admitting a contracting homotopy over a subalgebra $B\subset A$. In settings of the relative homological algebra, the Hochschild cocycle corresponding to the sequence $E$ is described explicitly. The “absolute case” has been earlier investigated by V. Dlab and C. M. Ringel. Being applied to that case, the present investigation gives a shorter arguments than that of Dlab–Ringel's work. 
@article{ZNSL_2006_330_a1,
     author = {E. A. Bezyakina and A. I. Generalov},
     title = {Cocycles in the relative {Hochschild} cohomology},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {29--35},
     year = {2006},
     volume = {330},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a1/}
}
TY  - JOUR
AU  - E. A. Bezyakina
AU  - A. I. Generalov
TI  - Cocycles in the relative Hochschild cohomology
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2006
SP  - 29
EP  - 35
VL  - 330
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a1/
LA  - ru
ID  - ZNSL_2006_330_a1
ER  - 
%0 Journal Article
%A E. A. Bezyakina
%A A. I. Generalov
%T Cocycles in the relative Hochschild cohomology
%J Zapiski Nauchnykh Seminarov POMI
%D 2006
%P 29-35
%V 330
%U http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a1/
%G ru
%F ZNSL_2006_330_a1
E. A. Bezyakina; A. I. Generalov. Cocycles in the relative Hochschild cohomology. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 29-35. http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a1/

[1] G. Hochschild, “Relative homological algebra”, Trans. Amer. Math. Soc., 82:1 (1956), 246–269 | DOI | MR | Zbl

[2] V. Dlab, C. M. Ringel, “The Hochschild cocycle corresponding to a long exact sequence”, Tsukuba J. Math., 14:2 (1990), 489–496 | MR | Zbl

[3] S. Maklein, Gomologiya, Mir, M., 1966