Enveloping -algebras and derivations of Baer JB-algebras

Abstract

In this paper, we prove that under certain conditions the enveloping $*$-algebra of an AJW-algebra is an AW${}^{*}$-algebra. Applying this, we prove that an extension of a derivation of a reversible JC-algebra A to a $*$-derivation of the C${}^{*}$-algebra generated by A is unique, and reversible AJW-algebras, satisfying certain conditions, have only inner derivations.

Keywords:

• AJW-algebra
• AW${}^{*}$-algebra
• derivation
• enveloping $*$-algebra
• inner derivation
• real C${}^{*}$-algebra

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17C65
• 46L57