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Homological dimensions and approximate contractibility for Köthe algebras

100%

Pirkovskii A.

Banach Center Publications

2010

tom 91

nr 1

261-278

We give a survey of our recent results on homological properties of Köthe algebras, with an emphasis on biprojectivity, biflatness, and homological dimension. Some new results on the approximate contractibility of Köthe algebras are also presented.

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

63%

Pirkovskii A., Selivanov Y.

Banach Center Publications

2010

tom 91

nr 1

279-313

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.

Ograniczanie wyników

2 Banach Center Publications

2 Pirkovskii A.

1 Selivanov Y.

2 2010

Wyniki wyszukiwania

Homological dimensions and approximate contractibility for Köthe algebras

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