On Certain Semiprime Associative Superalgebras
-
1
Universidad de La Rioja
info
ISSN: 0092-7872
Any de publicació: 2009
Volum: 37
Número: 10
Pàgines: 3548-3552
Tipus: Article
Altres publicacions en: Communications in Algebra
Projectes relacionats
Resum
In this note we emphasise the relationship between the structure of an associative superalgebra with superinvolution and the structure of the Lie substructure of skewsymmetric elements. More explicitly, we show that if A is a semiprime associative superalgebra with superinvolution and K is the Lie superalgebra of skewsymmetric elements satisfying [K<sup>2</sup>, K<sup>2</sup>] = 0, then A is a subdirect product of orders in simple superalgebras each at most 4-dimensional over its center