東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Local and Analytic Cyclic Homology

Meyer, Ralf,

FindBook

Google Book

Amazon

博客來

Local and Analytic Cyclic Homology

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Local and Analytic Cyclic Homology/ Ralf Meyer
作者:	Meyer, Ralf,
出版者:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2007,
面頁冊數:	1 online resource (368 pages)
標題:	Algebraic geometry -
電子資源:	https://doi.org/10.4171/039
電子資源:	https://www.ems-ph.org/img/books/meyer_mini.jpg
ISBN:	9783037195390

Local and Analytic Cyclic Homology
Meyer, Ralf,

Local and Analytic Cyclic Homology[electronic resource] /Ralf Meyer - Zuerich, Switzerland :European Mathematical Society Publishing House,2007 - 1 online resource (368 pages) - EMS Tracts in Mathematics (ETM)3.

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

Periodic cyclic homology is a homology theory for non-commutative algebras that plays a similar role in non-commutative geometry as de Rham cohomology for smooth manifolds. While it produces good results for algebras of smooth or polynomial functions, it fails for bigger algebras such as most Banach algebras or C*-algebras. Analytic and local cyclic homology are variants of periodic cyclic homology that work better for such algebras. In this book the author develops and compares these theories, emphasising their homological properties. This includes the excision theorem, invariance under passage to certain dense subalgebras, a Universal Coefficient Theorem that relates them to K-theory, and the Chern-Connes character for K-theory and K-homology. The cyclic homology theories studied in this text require a good deal of functional analysis in bornological vector spaces, which is supplied in the first chapters. The focal points here are the relationship with inductive systems and the functional calculus in non-commutative bornological algebras. The book is mainly intended for researchers and advanced graduate students interested in non-commutative geometry. Some chapters are more elementary and independent of the rest of the book, and will be of interest to researchers and students working in functional analysis and its applications.

ISBN: 9783037195390

Standard No.: 10.4171/039doiSubjects--Topical Terms:

3480846
Algebraic geometry

Local and Analytic Cyclic Homology
LDR:02387nmm a22003135a 4500 001 2233163
003 CH-001817-3
005 20091109150325.0
006 a fot ||| 0|
007 cr nn mmmmamaa
008 210928e20070806sz fot ||| 0|eng d
020 $a 9783037195390
024 7 0 $a 10.4171/039 $2 doi
035 $a 59-091109
040 $a ch0018173
072 7 $a PBMW $2 bicssc
072 7 $a PBKG $2 bicssc
084 $a 19-xx $a 46-xx $2 msc
100 1 $a Meyer, Ralf, $e author. $3 3480891
245 1 0 $a Local and Analytic Cyclic Homology $h [electronic resource] / $c Ralf Meyer
260 3 $a Zuerich, Switzerland : $b European Mathematical Society Publishing House, $c 2007
300 $a 1 online resource (368 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 0 $a EMS Tracts in Mathematics (ETM) $v 3
506 1 $a Restricted to subscribers: $u https://www.ems-ph.org/ebooks.php
520 $a Periodic cyclic homology is a homology theory for non-commutative algebras that plays a similar role in non-commutative geometry as de Rham cohomology for smooth manifolds. While it produces good results for algebras of smooth or polynomial functions, it fails for bigger algebras such as most Banach algebras or C*-algebras. Analytic and local cyclic homology are variants of periodic cyclic homology that work better for such algebras. In this book the author develops and compares these theories, emphasising their homological properties. This includes the excision theorem, invariance under passage to certain dense subalgebras, a Universal Coefficient Theorem that relates them to K-theory, and the Chern-Connes character for K-theory and K-homology. The cyclic homology theories studied in this text require a good deal of functional analysis in bornological vector spaces, which is supplied in the first chapters. The focal points here are the relationship with inductive systems and the functional calculus in non-commutative bornological algebras. The book is mainly intended for researchers and advanced graduate students interested in non-commutative geometry. Some chapters are more elementary and independent of the rest of the book, and will be of interest to researchers and students working in functional analysis and its applications.
650 0 7 $a Algebraic geometry $2 bicssc $3 3480846
650 0 7 $a Functional analysis $3 731345
650 0 7 $a $K$-theory $2 msc $3 3480892
856 4 0 $u https://doi.org/10.4171/039
856 4 2 $3 cover image $u https://www.ems-ph.org/img/books/meyer_mini.jpg