This article is cited in 3 papers

Structure of singular superalgebras with $2$-dimensional even part and new examples of singular superalgebras

S. V. Pchelintsev, O. V. Shashkov

Financial University under the Government of the Russian Federation, Moscow

Abstract: 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.

UDC: 512.554.5

Received: 19.06.2022
Revised: 13.10.2023

DOI: 10.33048/alglog.2022.61.605

 English version: Algebra and Logic, 2022, 61:6, 506–523