representation theory

representation theory (countable and uncountable, plural representation theories)

1. (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.
   • 1989 [Clarendon Press], Robert J. Baston, Michael G. Eastwood, The Penrose Transform: Its Interaction with Representation Theory, 2016 Dover edition.
   • 1998, A. Broer, A. Daigneault, Representation Theories and Algebraic Geometry, Springer:
   • 2005, Andrea Brini, Francesco Regonati, Antonio Teolis, Combinatorics and Representation Theory of Lie Superalgebras over Letterplace Superalgebras, Hongbo Li, Peter J. Olver, Gerald Sommer (editors), Computer Algebra and Geometric Algebra with Applications: 6th International Workshop IWWM and International Workshop GIAE, Springer, LNCS 3519, page 239,

     As an application, we describe in detail the way to specialize general results to the representation theory of the symmetric group and to classical invariant theory.

   • 2005, Ragnar-Olaf Buchweitz, Helmut Lenzing, Representations of Algebras and Related Topics, American Mathematical Society, page ix:

     From his numerous contributions through research articles, books, and conference volumes we just mention his^{[Vlastimil Dlab's]} work on the representation theory of hereditary algebras in the mid-seventies of the last century, joint with C.M. Ringel, laying the foundations of, in particular, tame hereditary representation theory over arbitrary fields, a theory still at the centre of interest.

Almost always used in the singular, but often qualified by the category of structure represented.

• category theory