Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

ELEMENTARY OPERATORS AS LIE HOMOMORPHISMS OR COMMUTATIVITY PRESERVERS

Matej Brešara1 and Peter Šemrla2

a1 Department of Mathematics, University of Maribor, PEF, Koroška 160, SI-2000 Maribor, Slovenia (bresar@uni-mb.si)

a2 Department of Mathematics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia (peter.semrl@fmf.uni-lj.si)

Abstract

We consider elementary operators on centrally closed prime algebras that are Lie (or Jordan) homomorphisms or commutativity preservers.

AMS 2000 Mathematics subject classification: Primary 16N60. Secondary 16R50; 47B47

(Received February 16 2004)

Keywords

  • elementary operator;
  • Lie homomorphism;
  • Jordan homomorphism;
  • commutativity preserver;
  • centrally closed prime algebra