Structure theory of homologically trivial and annihilator locally C*-algebras

Details Structure theory of homologically trivial and annihilator locally C*-algebras Structure theory of homologically trivial and annihilator locally C*-algebras

2010-06-20

arxiv.org/abs/1006.3934v1

Mathematics

Operator Algebras

35 pages

Scientific paper

We study the structure of certain classes of homologically trivial locally C*-algebras. These include algebras with projective irreducible Hermitian A-modules, biprojective algebras, and superbiprojective algebras. We prove that, if A is a locally C*-algebra, then all irreducible Hermitian A-modules are projective if and only if A is a direct topological sum of elementary C*-algebras. This is also equivalent to A being an annihilator (dual, complemented, left quasi-complemented, or topologically modular annihilator) topological algebra. We characterize all annihilator $\sigma$-C*-algebras and describe the structure of biprojective locally C*-algebras. Also, we present an example of a biprojective locally C*-algebra that is not topologically isomorphic to a Cartesian product of biprojective C*-algebras. Finally, we show that every superbiprojective locally C*-algebra is topologically *-isomorphic to a Cartesian product of full matrix algebras.

Affiliated with

Also associated with

No associations

Rating

Structure theory of homologically trivial and annihilator locally C*-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 Structure theory of homologically trivial and annihilator locally C*-algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Structure theory of homologically trivial and annihilator locally C*-algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-186087