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The existence of superinvolutions

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Publication Date
Volume
319
Issue
10
Identifiers
DOI: 10.1016/j.jalgebra.2007.10.044
Keywords
  • Superinvolution
  • Albert Theorem
  • Albert–Riehm Theorem
  • Superalgebra
  • Simple
  • Central
Disciplines
  • Mathematics

Abstract

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.

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