Lie derivations of triangular algebras without assuming unity

ABSTRACT

In this paper we initiate the study of mapping problems on triangular algebras without assuming unity. We give the definitions of strong faithful bimodules, extreme centres, and extreme Lie derivations. Our main result is to give a description of Lie derivations on triangular algebras without assuming unity. As an application we shall give a characterization of Lie derivations on upper triangular matrix algebras over a faithful algebra.

COMMUNICATED BY:

• T.-Y. Tam

Keywords:

• Triangular algebra
• strong faithful bimodule
• Lie derivation
• extreme Lie derivation
• derivation

2010 Mathematics Subject Classifications:

• 16W25
• 15A78

Acknowledgements

The author would like to thank the referee for many valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author.