Geodesic
Faithful representations of finite type for conformal Lie algebras
Algebra i logika, Tome 62 (2023) no. 3, pp. 408-414.

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

@article{AL_2023_62_3_a4,
     author = {R. A. Kozlov},
     title = {Faithful representations of finite type for conformal {Lie} algebras},
     journal = {Algebra i logika},
     pages = {408--414},
     publisher = {mathdoc},
     volume = {62},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2023_62_3_a4/}
}
TY  - JOUR
AU  - R. A. Kozlov
TI  - Faithful representations of finite type for conformal Lie algebras
JO  - Algebra i logika
PY  - 2023
SP  - 408
EP  - 414
VL  - 62
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2023_62_3_a4/
LA  - ru
ID  - AL_2023_62_3_a4
ER  - 
%0 Journal Article
%A R. A. Kozlov
%T Faithful representations of finite type for conformal Lie algebras
%J Algebra i logika
%D 2023
%P 408-414
%V 62
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2023_62_3_a4/
%G ru
%F AL_2023_62_3_a4
R. A. Kozlov. Faithful representations of finite type for conformal Lie algebras. Algebra i logika, Tome 62 (2023) no. 3, pp. 408-414. http://geodesic.mathdoc.fr/item/AL_2023_62_3_a4/

[1] P. S. Kolesnikov, R. A. Kozlov, A. S. Panasenko, “Quadratic Lie conformal superalgebras related to Novikov superalgebras”, J. Noncommut. Geom., 15:4 (2021), 1485–1500 | DOI | MR | Zbl

[2] J. Mostovoy, J. M. Pérez-Izquierdo, I. P. Shestakov, “Hopf algebras in non-associative Lie theory”, Bull. Math. Sci., 4:1 (2014), 129–173 | DOI | MR | Zbl

[3] P. Kolesnikov, “On finite representations of conformal algebras”, J. Algebra, 331:1 (2011), 169–193 | DOI | MR | Zbl

[4] P. Kolesnikov, “The Ado theorem for finite Lie conformal algebras with Levi decomposition”, J. Algebra Appl., 15:7 (2016), 1650130, 13 pp. | DOI | MR | Zbl

[5] B. Bakalov, V. G. Kac, A. A. Voronov, “Cohomology of conformal algebras”, Commun. Math. Phys., 200:3 (1999), 561–589 | DOI | MR

[6] S.-J. Cheng, V. G. Kac, M. Wakimoto, “Extensions of conformal modules”, Topological field theory, primitive forms and related topics, Proc. 38th Taniguchi symp.; RIMS symp. (Kyoto, Japan, December 9–13, 1996; Kyoto, Japan, December 16–19, 1996), Prog. Math., 160, eds. M. Kashiwara et al., Birkhäuser, Boston, MA, 1998, 79–129 | Zbl

[7] M. Roitman, “On free conformal and vertex algebras”, J. Algebra, 217:2 (1999), 496–527 | DOI | MR | Zbl

[8] R. Kozlov, On universal conformal envelopes for quadratic conformal algebras, arXiv: 2212.03532v1

[9] P. S. Kolesnikov, R. A. Kozlov, “Standard bases for the universal associative conformal envelopes of Kac–Moody conformal algebras”, Algebr. Represent. Theory, 25:4 (2022), 847–867 | DOI | MR | Zbl

[10] P. Kolesnikov, “Gröbner–Shirshov bases for associative conformal algebras with arbitrary locality function”, New trends in algebras and combinatorics, ICAC 2017, Proc. 3rd int. congr. algebras and combinatorics (Hong Kong, China, August 25–28, 2017), eds. K. P. Shum et al., World Scientific, Hackensack, NJ, 2020, 255–267 | DOI | MR | Zbl

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

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

[13] C. Boyallian, V. G. Kac, J.-I. Liberati, “On the classification of subalgebras of $\mathrm{Cend}_N$ and $\mathrm{gc}_N$”, J. Algebra, 260:1 (2003), 32–63 | DOI | MR | Zbl

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

[15] I. A. Dolguntseva, “Trivialnost vtoroi gruppy kogomologii konformnykh algebr $\mathrm{Cend}_n$ i $\mathrm{Cur}_n$”, Algebra i analiz, 21:1 (2009), 74–89 | MR

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

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

[18] R. A. Kozlov, “Kogomologii Khokhshilda assotsiativnoi konformnoi algebry $\mathrm{Cend}_{1,x}$”, Algebra i logika, 58:1 (2019), 52–68 | MR | Zbl

[19] P. S. Kolesnikov, R. A. Kozlov, “On the Hochschild cohomologies of associative conformal algebras with a finite faithful representation”, Commun. Math. Phys., 369:1 (2019), 351–370 | DOI | MR | Zbl