Abstract view
Jordan $*$Derivations of FiniteDimensional Semiprime Algebras


Published:20120727
Printed: Mar 2014
Ajda Fošner,
Faculty of Management, University of Primorska, Cankarjeva 5, SI6104 Koper, Slovenia
TsiuKwen Lee,
Department of Mathematics, National Taiwan University, Taipei 106, Taiwan
Abstract
In the paper, we characterize Jordan $*$derivations of a $2$torsion
free, finitedimensional semiprime algebra $R$ with involution $*$. To
be precise, we prove the theorem: Let $deltacolon R o R$ be a Jordan
$*$derivation. Then there exists a $*$algebra decomposition
$R=Uoplus V$ such that both $U$ and $V$ are invariant under
$delta$. Moreover, $*$ is the identity map of $U$ and $delta,_U$ is a
derivation, and the Jordan $*$derivation $delta,_V$ is inner.
We also prove the theorem: Let $R$ be a noncommutative, centrally
closed prime algebra with involution $*$, $operatorname{char},R
e 2$,
and let $delta$ be a nonzero Jordan $*$derivation of $R$. If $delta$ is
an elementary operator of $R$, then $operatorname{dim}_CRlt infty$ and
$delta$ is inner.
MSC Classifications: 
16W10, 16N60, 16W25 show english descriptions
Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx] Prime and semiprime rings [See also 16D60, 16U10] Derivations, actions of Lie algebras
16W10  Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx] 16N60  Prime and semiprime rings [See also 16D60, 16U10] 16W25  Derivations, actions of Lie algebras
