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Additional
representation theory
English Wikipedia - The Free Encyclopedia
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Representation theory
Representation theory
is 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. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by
matrices
and the
algebraic operations
in terms of
matrix addition
and
matrix multiplication
. The
algebraic
objects amenable to such a description include
groups
,
associative algebras
and
Lie algebras
. The most prominent of these (and historically the first) is the
representation theory of groups
, in which elements of a group are represented by invertible matrices in such a way that the group operation is matrix multiplication.
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