IDEALS OF GENERAL LINEAR LIE ALGEBRAS OF INFINITE-DIMENSIONAL VECTOR SPACES

Article Mathematics

Normal subgroups in the group of column-finite infinite matrices

Waldemar Holubowski et al.

Summary: The text discusses the study of normal subgroups of the GL(n, K) group, including cases where they are not contained in the center and specific descriptions of normal subgroups. It also mentions incomplete proofs in certain cases and fills the gap in one of them, providing a lattice description of normal subgroups.

JOURNAL OF GROUP THEORY (2022)

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Article Mathematics, Applied

Automorphisms and derivations of algebras of infinite matrices

Oksana Bezushchak

Summary: This article describes automorphisms and derivations of several important associative and Lie algebras of infinite matrices over a field. It provides some valuable references for studying the algebraic properties of infinite matrices.

LINEAR ALGEBRA AND ITS APPLICATIONS (2022)

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Article Mathematics

Derivations and automorphisms of locally matrix algebras

Oksana Bezushchak

Summary: The paper discusses derivations and automorphisms of infinite tensor products of matrix algebras, and shows that for a countable-dimensional locally matrix algebra, the dimension of the Lie algebra of outer derivations and the order of the group of outer automorphisms are both equal to vertical bar F vertical bar N-0, where vertical bar F vertical bar is the cardinality of the field F.

JOURNAL OF ALGEBRA (2021)

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Article Mathematics, Applied