representation theory
Noun
Meaning
representation theory (countable and uncountable, plural representation theories)
(mathematics, algebra) A branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.
Examples
Representation theory * The universal enveloping algebra of a Lie algebra is an associative algebra that can be used to study the given Lie algebra.
Kuipers 1999 Representation theory is both an application of the group concept and important for a deeper understanding of groups.
Representation theory also depends heavily on the type of vector space on which the group acts.
Representation theory studies the actions of algebraic objects on vector spaces by representing these objects as matrices.