Jordan *-derivations of finite-dimensional semiprime algebras
Journal
Canadian Mathematical Bulletin
Journal Volume
57
Journal Issue
1
Pages
51-60
Date Issued
2014
Author(s)
Fošner, A.
Abstract
In this paper, we characterize Jordan *-derivations of a 2-torsion free, finite-dimensional semiprime algebra R with involution *. To be precise, we prove the following. Let δ : R → R be a Jordan *-derivation. Then there exists a *-algebra decomposition R = U V such that both U and V are invariant under δ. Moreover, * is the identity map of U and δ |U is a derivation, and the Jordan *-derivation δ |V is inner. We also prove the following. Let R be a noncommutative, centrally closed prime algebra with involution *, char R ≠ 2, and let δ be a nonzero Jordan *-derivation of R. If δ is an elementary operator of R, then dimC R < ∞ and δ is inner. © Canadian Mathematical Society 2012.
Type
journal article