Geodesic
Structure of singular superalgebras with $2$-dimensional even part and new examples of singular superalgebras
Algebra i logika, Tome 61 (2022) no. 6, pp. 742-765

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

It is proved that a singular superalgebra with a $2$-dimensional even part is isomorphic to a superalgebra $B_{2\mid3}(\varphi,\xi,\psi)$. In particular, there do not exist infinite-dimensional simple singular superalgebra with a $2$-dimensional even part. It is proved that if a singular superalgebra contains an odd left annihilator, then it contains a nondegenerate switch. Lastly, it is established that for any number $N\geq 5$, except the numbers $6,7,8,11$, there exist singular superalgebras with a switch of dimension $N$. For the numbers $N=6,7,8,11$, there do not exist singular $N$-dimensional superalgebras with a switch.
Keywords: singular superalgebra with switch, extended double, singular superalgebra with $2$-dimensional even part. 
@article{AL_2022_61_6_a5,
     author = {S. V. Pchelintsev and O. V. Shashkov},
     title = {Structure of singular superalgebras with $2$-dimensional even part and new examples of singular superalgebras},
     journal = {Algebra i logika},
     pages = {742--765},
     publisher = {mathdoc},
     volume = {61},
     number = {6},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2022_61_6_a5/}
}
TY  - JOUR
AU  - S. V. Pchelintsev
AU  - O. V. Shashkov
TI  - Structure of singular superalgebras with $2$-dimensional even part and new examples of singular superalgebras
JO  - Algebra i logika
PY  - 2022
SP  - 742
EP  - 765
VL  - 61
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2022_61_6_a5/
LA  - ru
ID  - AL_2022_61_6_a5
ER  - 
%0 Journal Article
%A S. V. Pchelintsev
%A O. V. Shashkov
%T Structure of singular superalgebras with $2$-dimensional even part and new examples of singular superalgebras
%J Algebra i logika
%D 2022
%P 742-765
%V 61
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2022_61_6_a5/
%G ru
%F AL_2022_61_6_a5
S. V. Pchelintsev; O. V. Shashkov. Structure of singular superalgebras with $2$-dimensional even part and new examples of singular superalgebras. Algebra i logika, Tome 61 (2022) no. 6, pp. 742-765. http://geodesic.mathdoc.fr/item/AL_2022_61_6_a5/