S. V. Pchelintsev, O. V. Shashkov, “Singular 6-dimensional superalgebras”, Sib. Èlektron. Mat. Izv., 2018, Volume 15,Pages <nobr>92

This article is cited in 5 papers

Mathematical logic, algebra and number theory

Singular 6-dimensional superalgebras

S. V. Pchelintsev^ab, O. V. Shashkov^b

^a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
^b Financial University under the Government of the Russian Federation, Leningradsky pr., 49, 125993, Moscow, Russia

Abstract: A simple right alternative superalgebra is called singular if its even part is an algebra with zero multiplication. The first example of a 5-dimensional (this is the smallest possible dimension) singular superalgebra was given by J.P. da Silva, L.S.I. Murakami and I.P. Shestakov in 2016. In the previous paper we classified singular 5-dimensional superalgebras. It is proved that there are no 6-dimensional singular superalgebras.

Keywords: simple right alternative superalgebra, singular superalgebra.

UDC: 512.554.5

MSC: 17A70, 17D15

Received December 17, 2017, published February 8, 2018

DOI: 10.17377/semi.2018.15.011