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

Alexei 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 -