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

Alexei Yu. Pirkovskii; Yurii V. Selivanov

Banach Center Publications (2010)

- Volume: 91, Issue: 1, page 279-313
- ISSN: 0137-6934

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topAlexei Yu. Pirkovskii, and Yurii V. Selivanov. "Structure theory of homologically trivial and annihilator locally C*-algebras." Banach Center Publications 91.1 (2010): 279-313. <http://eudml.org/doc/282231>.

@article{AlexeiYu2010,

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 σ-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.},

author = {Alexei Yu. Pirkovskii, Yurii V. Selivanov},

journal = {Banach Center Publications},

keywords = {homologically trivial; locally -algebras},

language = {eng},

number = {1},

pages = {279-313},

title = {Structure theory of homologically trivial and annihilator locally C*-algebras},

url = {http://eudml.org/doc/282231},

volume = {91},

year = {2010},

}

TY - JOUR

AU - Alexei Yu. Pirkovskii

AU - Yurii V. Selivanov

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

JO - Banach Center Publications

PY - 2010

VL - 91

IS - 1

SP - 279

EP - 313

AB - 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 σ-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.

LA - eng

KW - homologically trivial; locally -algebras

UR - http://eudml.org/doc/282231

ER -

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