عنوان

Partial dynamical systems, Fell bundles and applications /

1470437856

9781470437855

Partial dynamical systems, Fell bundles and applications /

[Book]

Ruy Exel.

Providence, Rhode Island :

American Mathematical Society,

[2017]

©2017

vi, 321 pages :

illustrations ;

27 cm

Mathematical surveys and monographs ;

volume 224

Includes bibliographical references (pages 313-317) and subject index.

Part 1. Partial actions -- Part 2. Fell bundles -- Part 3. Applications.

0

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.

Banach spaces.

C*-algebras.

Isometrics (Mathematics)

Associative rings and algebras-- Rings and algebras arising under various constructions-- Smash products of general Hopf actions.

Associative rings and algebras-- Rings and algebras arising under various constructions-- Twisted and skew group rings, crossed products.

Banach spaces.

Banach, Espaces de.

C*-algebras.

C*-algèbres.

Functional analysis-- Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$- ) algebras, etc.)-- Decomposition theory for $C^*$-algebras.

Functional analysis-- Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$- ) algebras, etc.)-- Noncommutative dynamical systems.

Isometrics (Mathematics)

Isométrie (mathématiques)

Exel, Ruy,1956-

20200823025809.0

rda

[Book]

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