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Enveloping von Neumann algebra information


In operator algebras, the enveloping von Neumann algebra of a C*-algebra is a von Neumann algebra that contains all the operator-algebraic information about the given C*-algebra. This may also be called the universal enveloping von Neumann algebra, since it is given by a universal property; and (as always with von Neumann algebras) the term W*-algebra may be used in place of von Neumann algebra.

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Enveloping von Neumann algebra

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In operator algebras, the enveloping von Neumann algebra of a C*-algebra is a von Neumann algebra that contains all the operator-algebraic information...

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Enveloping algebra

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algebra Enveloping algebra, of an associative algebra: see Associative algebra § Enveloping algebra Enveloping von Neumann algebra, of a C*-algebra This...

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List of things named after John von Neumann

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norm Stone–von Neumann theorem Taylor–von Neumann–Sedov blast wave von Neumann algebra Abelian von Neumann algebra Enveloping von Neumann algebra Finite-dimensional...

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Group algebra of a locally compact group

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group C*-algebra defined above if and only if G is amenable. The group von Neumann algebra W*(G) of G is the enveloping von Neumann algebra of C*(G)....

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List of algebras

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algebra Symmetric algebra Tensor algebra Universal enveloping algebra Vertex operator algebra von Neumann algebra Weyl algebra Zinbiel algebra This is a list...

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Heisenberg group

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the reason is the Stone–von Neumann theorem: there is a unique unitary representation with given action of the central Lie algebra element z, up to a unitary...

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Glossary of ring theory

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the images. enveloping algebra The (universal) enveloping algebra E of a not-necessarily-associative algebra A is the associative algebra determined by...

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List of abstract algebra topics

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Non-associative algebra Universal enveloping algebra Lie algebra (see also list of Lie group topics and list of representation theory topics) Jordan algebra Alternative...

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Unitary representation

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corresponding to an elliptic differential operator D in the universal enveloping algebra of G, are analytic. Not only do smooth or analytic vectors form dense...

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List of theorems

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Birkhoff–Grothendieck theorem (complex geometry) Birkhoff–Von Neumann theorem (linear algebra) Birkhoff's representation theorem (lattice theory) Birkhoff's...

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Poisson bracket

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about is given in the universal enveloping algebra article. Quantum deformations of the universal enveloping algebra lead to the notion of quantum groups...

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Representation theorem

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universal enveloping algebra. Ado's theorem states that every finite-dimensional Lie algebra over a field of characteristic zero embeds into the Lie algebra of...

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List of representation theory topics

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Representation of a Lie group Lie algebra representation, Representation of a Lie superalgebra Universal enveloping algebra Casimir element Infinitesimal...

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Jacques Dixmier

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claim that Dixmier originated the name von Neumann algebra for the operator algebras introduced by John von Neumann, but Dixmier said in an interview that...

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Zonal spherical function

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(G)^{\prime \prime }P.} Thus the commutant of π is generated as a von Neumann algebra by operators P ρ ( f ) P = ∫ G f ( g ) ( P ρ ( g ) P ) d g {\displaystyle...

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Fourier transform

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respect to the largest possibly C*-norm gives its enveloping C*-algebra, called the group C*-algebra C*(G) of G. (Any C*-norm on L1(G) is bounded by the...

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Plancherel theorem for spherical functions

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the subspace H0 of K-invariant vectors in H. Moreover, the abelian von Neumann algebra it generates on H0 is maximal Abelian. By spectral theory, there...

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