Simple Right-Symmetric (1,1)-Superalgebras

Author(s)

Pozhidaev, A. P. ^[1] ; Shestakov, I. P. ^{[2, 1]}

Affiliation

^[1] Sobolev Inst Math, Novosibirsk - Russia

^[2] Univ Sao Paulo, Sao Paulo - Brazil

• Document type: Journal article
• Source: Algebra and Logic; v. 60, n. 2 SEP 2021.
• Web of Science Citations: 0

Abstract

It is proved that 2-torsion-free simple right-symmetric superrings having a nontrivial idempotent and satisfying a superidentity (x, y, z) + (-1)(z(x+y))(z, x, y) + (-1)(x(y+z))(y, z, x) = 0 are associative. As a consequence, every simple finitedimensional (1, 1)-superalgebra with semisimple even part over an algebraically closed field of characteristic 0 is associative. (AU)

• FAPESP's process: 18/23690-6 - Structures, representations, and applications of algebraic systems
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 18/05372-7 - Simple finite-dimensional left-symmetric (super)algebras
• Grantee: Ivan Chestakov
• Support Opportunities: Research Grants - Visiting Researcher Grant - International