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An introduction to C*-algebras and n...

Emerson, Heath.

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An introduction to C*-algebras and noncommutative geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	An introduction to C*-algebras and noncommutative geometry/ by Heath Emerson.
Author:	Emerson, Heath.
Published:	Cham :Springer International Publishing : : 2024.,
Description:	xiii, 539 p. :ill., digital ;24 cm.
[NT 15003449]:	An introduction to C-algebras -- An Introduction to Index Theory and Noncommutative Geometry -- Spectral Theory and Representation -- Positivity, Representations, Tensor Products and Ideals in C-algebras -- Module theory of C-algebras -- Morita Equivalence -- Topological K-theory and Clifford Algebras -- K-theory for Calgebras -- The Index Theorem of Atiyah and Singer -- K-homology and Noncommutative Geometry -- An Introduction to KK-theory -- Bibliography.
Contained By:	Springer Nature eBook
Subject:	C*-algebras. -
Online resource:	https://doi.org/10.1007/978-3-031-59850-0
ISBN:	9783031598500

An introduction to C*-algebras and noncommutative geometry
Emerson, Heath.

An introduction to C*-algebras and noncommutative geometry[electronic resource] /by Heath Emerson. - Cham :Springer International Publishing :2024. - xiii, 539 p. :ill., digital ;24 cm. - Birkhäuser advanced texts Basler Lehrbücher,2296-4894. - Birkhäuser advanced texts Basler Lehrbücher..

An introduction to C*-algebras -- An Introduction to Index Theory and Noncommutative Geometry -- Spectral Theory and Representation -- Positivity, Representations, Tensor Products and Ideals in C*-algebras -- Module theory of C*-algebras -- Morita Equivalence -- Topological K-theory and Clifford Algebras -- K-theory for C*algebras -- The Index Theorem of Atiyah and Singer -- K-homology and Noncommutative Geometry -- An Introduction to KK-theory -- Bibliography.

This is the first textbook on C*-algebra theory with a view toward Noncommutative Geometry. Moreover, it fills a gap in the literature, providing a clear and accessible account of the geometric picture of K-theory and its relation to the C*-algebraic picture. The text can be used as the basis for a graduate level or a capstone course with the goal being to bring a relative novice up to speed on the basic ideas while offering a glimpse at some of the more advanced topics of the subject. Coverage includes C*-algebra theory, K-theory, K-homology, Index theory and Connes' Noncommuntative Riemannian geometry. Aimed at graduate level students, the book is also a valuable resource for mathematicians who wish to deepen their understanding of noncommutative geometry and algebraic K-theory. A wide range of important examples are introduced at the beginning of the book. There are lots of excellent exercises and any student working through these will benefit significantly. Prerequisites include a basic knowledge of algebra, analysis, and a bit of functional analysis. As the book progresses, a little more mathematical maturity is required as the text discusses smooth manifolds, some differential geometry and elliptic operator theory, and K-theory. The text is largely self-contained though occasionally the reader may opt to consult more specialized material to further deepen their understanding of certain details.

ISBN: 9783031598500

Standard No.: 10.1007/978-3-031-59850-0doiSubjects--Topical Terms:

542530
C*-algebras.

LC Class. No.: QA326

Dewey Class. No.: 512.554

An introduction to C*-algebras and noncommutative geometry
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245 1 3 $a An introduction to C*-algebras and noncommutative geometry $h [electronic resource] / $c by Heath Emerson.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2024.
300 $a xiii, 539 p. : $b ill., digital ; $c 24 cm.
490 1 $a Birkhäuser advanced texts Basler Lehrbücher, $x 2296-4894
505 0 $a An introduction to C*-algebras -- An Introduction to Index Theory and Noncommutative Geometry -- Spectral Theory and Representation -- Positivity, Representations, Tensor Products and Ideals in C*-algebras -- Module theory of C*-algebras -- Morita Equivalence -- Topological K-theory and Clifford Algebras -- K-theory for C*algebras -- The Index Theorem of Atiyah and Singer -- K-homology and Noncommutative Geometry -- An Introduction to KK-theory -- Bibliography.
520 $a This is the first textbook on C*-algebra theory with a view toward Noncommutative Geometry. Moreover, it fills a gap in the literature, providing a clear and accessible account of the geometric picture of K-theory and its relation to the C*-algebraic picture. The text can be used as the basis for a graduate level or a capstone course with the goal being to bring a relative novice up to speed on the basic ideas while offering a glimpse at some of the more advanced topics of the subject. Coverage includes C*-algebra theory, K-theory, K-homology, Index theory and Connes' Noncommuntative Riemannian geometry. Aimed at graduate level students, the book is also a valuable resource for mathematicians who wish to deepen their understanding of noncommutative geometry and algebraic K-theory. A wide range of important examples are introduced at the beginning of the book. There are lots of excellent exercises and any student working through these will benefit significantly. Prerequisites include a basic knowledge of algebra, analysis, and a bit of functional analysis. As the book progresses, a little more mathematical maturity is required as the text discusses smooth manifolds, some differential geometry and elliptic operator theory, and K-theory. The text is largely self-contained though occasionally the reader may opt to consult more specialized material to further deepen their understanding of certain details.
650 0 $a C*-algebras. $3 542530
650 0 $a Noncommutative differential geometry. $3 629838
650 1 4 $a K-Theory. $3 897432
650 2 4 $a Topology. $3 522026
650 2 4 $a Differential Geometry. $3 891003
650 2 4 $a Dynamical Systems. $3 3538746
650 2 4 $a Functional Analysis. $3 893943
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830 0 $a Birkhäuser advanced texts Basler Lehrbücher. $3 3723285
856 4 0 $u https://doi.org/10.1007/978-3-031-59850-0
950 $a Mathematics and Statistics (SpringerNature-11649)