Complex representation

The term complex representation has slightly different meanings in mathematics and physics.

In mathematics, a complex representation is a group representation of a group (or Lie algebra) on a complex vector space.

In physics, a complex representation is a group representation of a group (or Lie algebra) on a complex vector space that is neither real nor pseudoreal. In other words, the group elements are expressed as complex matrices, and the complex conjugate of a complex representation is a different, non-equivalent representation. For compact groups, the Frobenius-Schur indicator can be used to tell whether a representation is real, complex, or pseudo-real.

For example, the N-dimensional fundamental representation of SU(N) for N greater than two is a complex representation whose complex conjugate is often called the antifundamental representation.

This algebra-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Algebra stubs Representation theory of groups Wikimedia Foundation. 2010. Игры ⚽ Нужно решить контрольную? Nessun dorma Hanalei Look at other dictionaries: Complex conjugate representation — In mathematics, if G is a group and ρ is a representation of it over the complex vector space V, then the complex conjugate representation ρ* is defined over the conjugate vector space V* as follows: ρ*(g) is the conjugate of ρ(g) for all g in G …   Wikipedia Representation ring — In mathematics, especially in the area of algebra known as representation theory, the representation ring of a group is a ring formed from all the (isomorphism classes of the) linear representations of the group. For a given group, the ring will… …   Wikipedia Complex system biology — Complex systems biology (CSB) is a branch or subfield of mathematical and theoretical biology concerned with complexity of both structure and function in biological organisms, as well as the emergence and evolution of organisms and species, with… …   Wikipedia Representation (arts) — Representation describes the signs that stand in for and take the place of something else.Mitchell, W. 1995, Representation , in F Lentricchia T McLaughlin (eds), Critical Terms for Literary Study , 2nd edn, University of Chicago Press, Chicago]… …   Wikipedia representation — refers to the way in which images and texts reconstruct, rather than reflect, the original sources they represent. Thus a painting, photograph, or written text about a tree is never an actual tree, but the reconstruction of what it seemed to be… …   Dictionary of sociology Representation theory of finite groups — In mathematics, representation theory is a technique for analyzing abstract groups in terms of groups of linear transformations. See the article on group representations for an introduction. This article discusses the representation theory of… …   Wikipedia Representation theory — This article is about the theory of representations of algebraic structures by linear transformations and matrices. For the more general notion of representations throughout mathematics, see representation (mathematics). Representation theory is… …   Wikipedia Complex number — A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the square root of –1. A complex… …   Wikipedia Representation of a Lie group — In mathematics and theoretical physics, the idea of a representation of a Lie group plays an important role in the study of continuous symmetry. A great deal is known about such representations, a basic tool in their study being the use of the… …   Wikipedia Representation theory of SL2(R) — In mathematics, the main results concerning irreducible unitary representations of the Lie group SL2(R) are due to Gelfand and Naimark (1946), V. Bargmann (1947), and Harish Chandra (1952). Structure of the complexified Lie algebra We choose a… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”