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nondegenerate representation

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  • 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

  • Spin representation — In mathematics, the spin representations are particular projective representations of the orthogonal or special orthogonal groups in arbitrary dimension and signature (i.e., including indefinite orthogonal groups). More precisely, they are… …   Wikipedia

  • Real representation — In the mathematical field of representation theory a real representation is usually a representation on a real vector space U , but it can also mean a representation on a complex vector space V with an invariant real structure, i.e., an… …   Wikipedia

  • Symplectic representation — In mathematical field of representation theory, a symplectic representation is a representation of a group or a Lie algebra on a symplectic vector space ( V , omega; ) which preserves the symplectic form omega; . Here omega; is a nondegenerate… …   Wikipedia

  • Gelfand-Naimark-Segal construction — In functional analysis, given a C* algebra A , the Gelfand Naimark Segal construction establishes a correspondence between cyclic * representations of A and certain linear functionals on A (called states ). The correspondence is shown by an… …   Wikipedia

  • Multiplier algebra — In C* algebras, the multiplier algebra, denoted by M(A), of a C* algebra A is a unital C* algebra which is the largest unital C* algebra that contains A as an ideal in a non degenerate way. It is the noncommutative generalization of Stone–Čech… …   Wikipedia

  • Clifford algebra — In mathematics, Clifford algebras are a type of associative algebra. They can be thought of as one of the possible generalizations of the complex numbers and quaternions.[1][2] The theory of Clifford algebras is intimately connected with the… …   Wikipedia

  • Bilinear form — In mathematics, a bilinear form on a vector space V is a bilinear mapping V × V → F , where F is the field of scalars. That is, a bilinear form is a function B : V × V → F which is linear in each argument separately::egin{array}{l} ext{1. }B(u + …   Wikipedia

  • Symplectic vector space — In mathematics, a symplectic vector space is a vector space V equipped with a nondegenerate, skew symmetric, bilinear form omega; called the symplectic form. Explicitly, a symplectic form is a bilinear form omega; : V times; V rarr; R which is *… …   Wikipedia

  • Spinor — In mathematics and physics, in particular in the theory of the orthogonal groups (such as the rotation or the Lorentz groups), spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the… …   Wikipedia

  • Symplectic matrix — In mathematics, a symplectic matrix is a 2n times; 2n matrix M (whose entries are typically either real or complex) satisfying the condition:M^T Omega M = Omega,.where MT denotes the transpose of M and Omega; is a fixed nonsingular, skew… …   Wikipedia

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