Hochschild cohomologies of the associative conformal algebra $\mathrm{Cend}_{1,x}$
Algebra i logika, Tome 58 (2019) no. 1, pp. 52-68.

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

It is stated that the second Hochshild cohomology group of the associative conformal algebra $\mathrm{Cend}_{1,x}$ with values in any bimodule is trivial. Consequently, the given algebra splits off in every extension with nilpotent kernel.
Mots-clés : associative conformal algebra
Keywords: split-off radical, Hochshild cohomologies.
@article{AL_2019_58_1_a3,
     author = {R. A. Kozlov},
     title = {Hochschild cohomologies of the associative conformal algebra $\mathrm{Cend}_{1,x}$},
     journal = {Algebra i logika},
     pages = {52--68},
     publisher = {mathdoc},
     volume = {58},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2019_58_1_a3/}
}
TY  - JOUR
AU  - R. A. Kozlov
TI  - Hochschild cohomologies of the associative conformal algebra $\mathrm{Cend}_{1,x}$
JO  - Algebra i logika
PY  - 2019
SP  - 52
EP  - 68
VL  - 58
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2019_58_1_a3/
LA  - ru
ID  - AL_2019_58_1_a3
ER  - 
%0 Journal Article
%A R. A. Kozlov
%T Hochschild cohomologies of the associative conformal algebra $\mathrm{Cend}_{1,x}$
%J Algebra i logika
%D 2019
%P 52-68
%V 58
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2019_58_1_a3/
%G ru
%F AL_2019_58_1_a3
R. A. Kozlov. Hochschild cohomologies of the associative conformal algebra $\mathrm{Cend}_{1,x}$. Algebra i logika, Tome 58 (2019) no. 1, pp. 52-68. http://geodesic.mathdoc.fr/item/AL_2019_58_1_a3/

[1] A. A. Belavin, A. M. Polyakov, A. V. Zamolodchikov, “Infinite conformai symmetry in two-dimensional quantum field theory”, Nucl. Phys. B, 241:2 (1984), 333–380 | MR | Zbl

[2] R. E. Borcherds, “Vertex algebras, Kac-Moody algebras, and the monster”, Proc. Natl. Acad. Sci. USA, 83 (1986), 3068–3071 | MR

[3] V. G. Kac, Vertex algebras for beginners, Univ. Lect. Ser., 10, 2nd ed., Am. Math. Soc., Providence, RI, 1998 | MR | Zbl

[4] A. D. Andrea, V. G. Kac, “Structure theory of finite conformai algebras”, Sel. Math., New Ser., 4:3 (1998), 377–418 | MR | Zbl

[5] S.-J. Cheng, V. G. Kac, “Conformai modules”, Asian J. Math., 1:1 (1997), 181–193 ; erratum, 2:1 (1998), 153–156 | MR | Zbl | MR

[6] E. I. Zelmanov, “On the structure of conformai algebras”, Combinatorial and computational algebra, Int. conf. on comb, and comput. algebra (Hong Kong, China, May 24–29, 1999), Contemp. Math., 264, eds. Kai Yuen Chan et al., Am. Math. Soc., Providence, RI, 2000, 139–153 | MR | Zbl

[7] E. I. Zel'manov, “Idempotents in conformai algebras”, Proc. 3d Int. Algebra Conf. (Tainan, Taiwan, June 16–July 1, 2002), eds. Yuen Fong et al., Kluwer Acad. Publ., Dordrecht, 2003, 257–266 | Zbl

[8] V. Bakalov, V. G. Kac, A. Voronov, “Cohomology of conformai algebras”, Comm. Math. Phys., 200:3 (1999), 561–598 | MR | Zbl

[9] P. S. Kolesnikov, “Associative conformai algebras with finite faithful representation”, Adv. Math., 202:2 (2006), 602–637 | MR | Zbl

[10] P. S. Kolesnikov, “On the Wedderburn principal theorem in conformal algebras”, J. Algebra Appl., 6:1 (2007), 119–134 | MR | Zbl

[11] I. A. Dolguntseva, “Kogomologii Khokhshilda dlya assotsiativnykh konformnykh algebr”, Algebra i logika, 46:6 (2007), 688–706 | Zbl

[12] I. A. Dolguntseva, “Trivialnost vtoroi gruppy kogomologii konformnykh algebr Cend$_n$ i Sur$_n$”, Algebra i analiz, 21:1 (2009), 74–89

[13] V. Bakalov, A. D'Andrea, V. G. Kac, “Theory of finite pseudoalgebras”, Adv. Math., 162:1 (2001), 1–140 | MR | Zbl

[14] L. A. Bokut', Yu. Fong, V.-F. Ke, P. S. Kolesnikov, “Bazisy Grebnera i Grebnera-Shirshova v algebre i konformnye algebry”, Fundament. i prikl. matem., 6:3 (2000), 669–706 | Zbl