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Partial Dynamical Systems, Fell Bundles and Applications

Ruy Exel
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      Partial dynamical systems, originally developed as a tool to study algebras of operators in Hilbert spaces, has recently become an important branch of algebra. Its most powerful results allow for understanding structural properties of algebras, both in the purely algebraic and in the C*-contexts, in terms of the dynamical properties of certain systems which are often hiding behind algebraic structures. The first indication that the study of an algebra using partial dynamical systems may be helpful is the presence of a grading. While the usual theory of graded algebras often requires gradings to be saturated, the theory of partial dynamical systems is especially well suited to treat nonsaturated graded algebras which are in fact the source of the notion of ""partiality''. One of the main results of the book states that every graded algebra satisfying suitable conditions may be reconstructed from a partial dynamical system via a process called the partial crossed product.Running in parallel with partial dynamical systems, partial representations of groups are also presented and studied in depth.In addition to presenting main theoretical results, several specific examples are analyzed, including Wiener-Hopf algebras and graph C*-algebras.
      Format: Hardback CONTRIBUTORS: Ruy Exel EAN: 9781470437855 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2017-08-01 CITY: GENRE: MATHEMATICS / Mathematical Analysis WIDTH: 178 cm SPINE:

      Book Themes:

      Calculus and mathematical analysis

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      Ruy Exel, Universidade Federal de Santa Catarina, Florianopolis-SC, Brazil.
      Partial dynamical systems, originally developed as a tool to study algebras of operators in Hilbert spaces, has recently become an important branch of algebra. Its most powerful results allow for understanding structural properties of algebras, both in the purely algebraic and in the C*-contexts, in terms of the dynamical properties of certain systems which are often hiding behind algebraic structures. The first indication that the study of an algebra using partial dynamical systems may be helpful is the presence of a grading. While the usual theory of graded algebras often requires gradings to be saturated, the theory of partial dynamical systems is especially well suited to treat nonsaturated graded algebras which are in fact the source of the notion of ""partiality''. One of the main results of the book states that every graded algebra satisfying suitable conditions may be reconstructed from a partial dynamical system via a process called the partial crossed product.Running in parallel with partial dynamical systems, partial representations of groups are also presented and studied in depth.In addition to presenting main theoretical results, several specific examples are analyzed, including Wiener-Hopf algebras and graph C*-algebras.
      Format: Hardback CONTRIBUTORS: Ruy Exel EAN: 9781470437855 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2017-08-01 CITY: GENRE: MATHEMATICS / Mathematical Analysis WIDTH: 178 cm SPINE:

      Book Themes:

      Calculus and mathematical analysis

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      Be the first to write a review
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      Ruy Exel, Universidade Federal de Santa Catarina, Florianopolis-SC, Brazil.

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