9 papers
On Clifford Algebras of Infinite Dimensional Vector Spaces
Oksana Bezushchak
We describe derivations of the Clifford algebra of a nondegenerate quadratic form on a countable dimensional vector space over an algebraically closed field of characteristic not e…
Derivations of rings of infinite matrices
O. Bezushchak
We describe derivations of several important associative and Lie rings of infinite matrices over general rings of coefficients.
Locally standard measure algebras
Oksana Bezushchak, Bogdana Oliynyk
We parameterize countable locally standard measure algebras by pairs of a Steinitz number and a real number greater or equal to 1. This is an analog of the theorems of J.Dixmier an…
Ideals of general linear Lie algebras of infinite-dimensional vector spaces
Oksana Bezushchak, Waldemar Hołubowski, Bogdana Oliynyk
Let V be an infinite-dimensional vector space over a field of characteristic not equal to 2. We classify ideals of the Lie algebra gl(V) of all linear transformations of the space…
Derivations and automorphisms of locally matrix algebras
Oksana Bezushchak
We describe derivations and automorphisms of infinite tensor products of matrix algebras. Using this description we show that for a countable--dimensional locally matrix algebra $A…
Hamming spaces and locally matrix algebras
Oksana Bezushchak, Bogdana Oliynyk
We introduce an abstract definition of a Hamming space that generalizes standard Hamming spaces . We classify countable locally standard Hamming spa…
Morita equivalent unital locally matrix algebras
Oksana Bezushchak, Bogdana Oliynyk
We describe Morita equivalence of unital locally matrix algebras in terms of their Steinitz parametrization. Two countable dimensional unital locally matrix algebras are Morita equ…
On primary decompositions of unital locally matrix algebras
Oksana Bezushchak, Bogdana Oliynyk
We construct a unital locally matrix algebra of uncountable dimension that (1) does not admit a primary decomposition, (2) has an infinite locally finite Steinitz number. It gives…
Unital locally matrix algebras and Steinitz numbers
Oksana Bezushchak, Bogdana Oliynyk
An -algebra with unit is said to be a locally matrix algebra if an arbitrary finite collection of elements from lies in a subalgebra wit…