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Operator algebras, unitary representations, enveloping algebras, and invariant theory actes du colloque en l"honneur de Jacques Dixmier

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Published by Birkhäuser in Boston .
Written in English


  • Lie groups -- Congresses.,
  • Lie algebras -- Congresses.,
  • Operator algebras -- Congresses.,
  • Invariants -- Congresses.

Book details:

Edition Notes

Statementedited by Alain Connes ... [et al.].
SeriesProgress in mathematics ;, v. 92, Progress in mathematics (Boston, Mass.) ;, v. 92.
ContributionsDixmier, Jacques., Connes, Alain.
LC ClassificationsQA387 .O64 1990
The Physical Object
Paginationxvi, 579 p. ;
Number of Pages579
ID Numbers
Open LibraryOL1888357M
ISBN 100817634894, 3764334894
LC Control Number90049716

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Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. Volume 13 of Invariant means and finite representation theory of C [ast] - algebras, Nathanial Patrick Brown Memoirs of the American Mathematical Society, American Mathematical Society, . In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator for every g ∈ general theory is well-developed in case G is a locally compact (Hausdorff) topological group and the representations are strongly continuous.. The theory has been widely applied in quantum mechanics since the s. Theory of Operator Algebras III Masamichi Takesaki (auth.) to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 's and 's.

Abstract. This chapter deals with *-representations of enveloping algebras. Though some of the considerations and of the main results (e.g., Theorem ) are valid for general *-representations, we aim to present a detailed study of integrable representations.   It is well known today that the theory of vertex operator algebra unifies representation theory of many infinite dimensional Lie algebras via locality. So it is natural to have a notion of unitary vertex operator algebra so that in the case of Virasoro and affine Kac–Moody algebras, these two unitarities are equivalent.   Abstract. In this chapter we collect background material on quantized universal enveloping algebras. We give in particular a detailed account of the construction of the braid group action and PBW-bases, and discuss the finite dimensional representation theory in the setting that the base field \(\mathbb {K} \) is an arbitrary field and the deformation parameter \(q \in \mathbb . C ∗-algebras (pronounced "C-star") are subjects of research in functional analysis, a branch of mathematics.A C*-algebra is a Banach algebra together with an involution satisfying the properties of the adjoint.A particular case is that of a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties. A is a topologically closed set in the norm.

  Operator Algebras, Unitary Representations, Envelping Algebras, and Invariant Theory, Progress in Mathematics, 92, Birkhauser, Boston () p. – Google Scholar. Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more. Operator algebras, unitary representations, enveloping algebras, and invariant theory: actes du colloque en l'honneur de Jacques Dixmier in SearchWorks catalog. *-algebras of unbounded operators in Hilbert space, or more generally algebraic systems of unbounded operators, occur in a natural way in unitary representation theory of Lie groups and in the Wightman formulation of quantum field theory. In representation theory they appear as the images of the associated representations of the Lie algebras or. The book provides a comprehensive treatment of the theory of operator algebras and representations on indefinite metric spaces and of its applications to the theory of *-derivations of C*-algebras.