Lie algebra of column-finite infinite matrices: ideals and derivations
Waldemar Ho{\l}ubowski, Sebastian \.Zurek
TL;DR
This paper investigates the structure of the Lie algebra formed by column-finite infinite matrices, detailing its ideals and derivations over various fields and rings, enhancing understanding of its algebraic properties.
Contribution
It characterizes the lattice of ideals and describes derivations of the Lie algebra of column-finite infinite matrices over arbitrary fields and rings.
Findings
Lattice of ideals explicitly described
Derivations of the Lie algebra classified
Results hold over arbitrary fields and rings
Abstract
In this paper we shall consider the Lie algebra of column-finite infinite matrices indexed by positive integers , describe the lattice of its ideals for arbitrary field and study its derivations over any commutative, unital ring .
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Taxonomy
TopicsAdvanced Topics in Algebra · graph theory and CDMA systems · Algebraic structures and combinatorial models