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Structure theory of homologically trivial and annihilator locally C*-algebras | | Alexei Yu. Pirkovskii
; Yurii V. Selivanov
; | | Date: |
20 Jun 2010 | | Abstract: | 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. | | Source: | arXiv, 1006.3934 | | Services: | Forum | Review | PDF | Favorites | |
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