vix.ing · top · new · best · stats · spec

The existence of superinvolutions

2007/04/24 by Alberto Elduque, Elduque, Alberto, Oliver Villa +1
Mathematics · Physics and Astronomy · #16W10 #16W55 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA) #math.RA #msc:16W10 #msc:16W55

paper · pdf · doi:10.48550/arxiv.0704.3127

21 pages

arxiv created 2007/04/24 · openalex publication_date 2007/04/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Superinvolutions on graded associative algebras constitute a source of Lie and Jordan superalgebras. Graded versions of the classical Albert and Albert-Riehm Theorems on the existence of superinvolutions are proven. Surprisingly, the existence of superinvolutions of the first kind is a rare phenomenon, as nontrivial central division superalgebras are never endowed with this kind of superinvolutions.

Related