Partial dynamical systems, Fell bundles and applications

著者

• Exel, Ruy

書誌事項

Partial dynamical systems, Fell bundles and applications

Ruy Exel

（Mathematical surveys and monographs, v. 224）

American Mathematical Society, c2017

注記

Includes bibliographical references (p. 313-317) and index

内容説明・目次

内容説明

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.

目次

Introduction Partial actions: Partial actions Restriction and globalization Inverse semigroups Topological partial dynamical sysytems Algebraic partial dynamical systems Multipliers Crossed products Partial group representations Partial group algebras C*-algebraic partial dynamical systems Partial isometries Covariant representations of C*-algebraic dynamical systems Partial representations subject to relations Hilbert modules and Morita-Rieffel-equivalence Fell bundles: Fell bundles Reduced cross-sectional algebras Fell's absorption principle Graded C*-algebras Amenability for Fell bundles Functoriality for Fell bundles Functoriality for partial actions Ideals in graded algebras Pre-Fell-bundles Tensor products of Fell bundles Smash product Stable Fell bundles as partial crossed products Globalization in the C*-context Topologically free partial actions Applications: Dilating partial representations Semigroups of isometries Quasi-lattice ordered groups C*-algebras generated by semigroups of isometries Wiener-Hopf C*-algebras The Toeplitz C*-algebra of a graph Path spaces Graph C*-algebras Bibliography Index.

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詳細情報

• NII書誌ID(NCID): BB24499817
• ISBN:
  • 9781470437855
• LCCN: 2017013411
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: vi, 321 p.
• 大きさ: 27 cm
• 分類:
  • LCC : QA326
  • DC23 : 515/.7
• 件名:
  • LCSH : C*-algebras
  • LCSH : Banach spaces
  • LCSH : Isometrics (Mathematics)
• 親書誌ID:
  • BA00134419