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

• Autorzy: Alexei Yu. Pirkovskii , Yurii V. Selivanov
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46M20: Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
• 46H25: Normed modules and Banach modules, topological modules (if not placed in \SbjNo 13-XX or \SbjNo 16-XX)
• 46H20: Structure, classification of topological algebras
• 46M10: Projective and injective objects

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 91
• Numer: 1
• Strony: 279-313

Daty

wydano

2010

Twórcy

autor

Alexei Yu. Pirkovskii

• Department of Geometry and Topology, Faculty of Mathematics, State University - Higher School of Economics, Vavilova 7, 117312 Moscow, Russia

autor

Yurii V. Selivanov

• Department of Higher Mathematics, Russian State Technological University (MATI), Orshanskaya 3, Moscow 121552, Russia

Identyfikatory

DOI

10.4064/bc91-0-17