Lie Algebras of Derivations and Resolvent Algebras

Details Lie Algebras of Derivations and Resolvent Algebras Lie Algebras of Derivations and Resolvent Algebras

2012-02-13

arxiv.org/abs/1202.2780v1

Physics

Mathematical Physics

14 pages

Scientific paper

This paper analyzes the action {\delta} of a Lie algebra X by derivations on a C*-algebra A. This action satisfies an "almost inner" property which ensures affiliation of the generators of the derivations {\delta} with A, and is expressed in terms of corresponding pseudo-resolvents. In particular, for an abelian Lie algebra X acting on a primitive C*-algebra A, it is shown that there is a central extension of X which determines algebraic relations of the underlying pseudo- resolvents. If the Lie action {\delta} is ergodic, i.e. the only elements of A on which all the derivations in {\delta}_x vanish are multiples of the identity, then this extension is given by a (non-degenerate) symplectic form {\sigma} on X. Moreover, the algebra generated by the pseudo-resolvents coincides with the resolvent algebra based on the symplectic space (X, {\sigma}). Thus the resolvent algebra of the canonical commutation relations, which was recently introduced in physically motivated analyses of quantum systems, appears also naturally in the representation theory of Lie algebras of derivations acting on C*-algebras.

Affiliated with

Also associated with

No associations

Rating

Lie Algebras of Derivations and Resolvent Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Lie Algebras of Derivations and Resolvent Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lie Algebras of Derivations and Resolvent Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-682782