Geodesic
Algebraically generated superalgebras
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2021), pp. 67-83.

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

A simple right-alternative superalgebra whose even part has zero multiplication is called singular. In the paper, finite-dimensional algebraically generated singular superalgebras with a non-degenerate switch are introduced and studied. A special case of such algebras, namely, linearly generated superalgebras, was previously classified by the authors. The construction of the extended double is given in the paper and it is proved that an algebraically generated singular superalgebra with a non-degenerate switch is an extended double. It is also shown that for any number $d\geq32$ there exists a $d$ -dimensional extended double.
Keywords: simple right-alternative superalgebra, singular superalgebra, non-degenerate switch, extended double. 
@article{IVM_2021_6_a6,
     author = {S. V. Pchelintsev and O. V. Shashkov},
     title = {Algebraically generated superalgebras},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {67--83},
     publisher = {mathdoc},
     number = {6},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_6_a6/}
}
TY  - JOUR
AU  - S. V. Pchelintsev
AU  - O. V. Shashkov
TI  - Algebraically generated superalgebras
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2021
SP  - 67
EP  - 83
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2021_6_a6/
LA  - ru
ID  - IVM_2021_6_a6
ER  - 
%0 Journal Article
%A S. V. Pchelintsev
%A O. V. Shashkov
%T Algebraically generated superalgebras
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2021
%P 67-83
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2021_6_a6/
%G ru
%F IVM_2021_6_a6
S. V. Pchelintsev; O. V. Shashkov. Algebraically generated superalgebras. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2021), pp. 67-83. http://geodesic.mathdoc.fr/item/IVM_2021_6_a6/

[1] Zelmanov E. I., Shestakov I. P., “Pervichnye alternativnye superalgebry i nilpotentnost radikala svobodnoi alternativnoi algebry”, Izv. AN SSSR. Cer. matem., 54:4 (1990), 676–693 | Zbl

[2] da Silva J. P., Murakami L. S.I., Shestakov I. P., “On right alternative syperalgebras”, Comm. Algebra, 44 (2016), 240–252 | DOI | MR | Zbl

[3] Pchelintsev S. V., Shashkov O. V., “Prostye 5-mernye pravoalternativnye superalgebry s trivialnoi chetnoi chastyu”, Sib. matem. zhurn., 58:6 (2017), 1078—1089 | MR | Zbl

[4] Pchelintsev S. V., Shashkov O. V., “Singulyarnye 6-mernye superalgebry”, SEMI, 15 (2018), 92–105 http://semr.math.nsc.ru | Zbl

[5] Pchelintsev S. V., Shashkov O. V., “Linearly generated singular superalgebras”, J. Algebra, 546 (2020), 580–603 | DOI | MR | Zbl

[6] Kleinfeld E., “Right alternative rings”, Proc. Amer. Math. Soc., 4:6 (1953), 939–944 | DOI | MR | Zbl

[7] Maltsev A. I., Osnovy lineinoi algebry, Nauka, M., 2005 | MR

[8] Dzhekobson N., Algebry Li, Mir, M., 1964