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001450509 001__ 1450509
001450509 003__ OCoLC
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001450509 019__ $$a1348493737
001450509 020__ $$a9783031055133$$q(electronic bk.)
001450509 020__ $$a3031055136$$q(electronic bk.)
001450509 020__ $$z9783031055126
001450509 020__ $$z3031055128
001450509 0247_ $$a10.1007/978-3-031-05513-3$$2doi
001450509 035__ $$aSP(OCoLC)1348377405
001450509 040__ $$aYDX$$beng$$erda$$epn$$cYDX$$dGW5XE$$dEBLCP$$dOCLCF$$dOCLCQ
001450509 049__ $$aISEA
001450509 050_4 $$aQA326
001450509 08204 $$a512/.55$$223/eng/20221101
001450509 1001_ $$aExel, Ruy,$$d1956-$$eauthor.
001450509 24510 $$aCharacterizing groupoid C* -algebras of non-Hausdorff Étale groupoids /$$cRuy Exel, David R. Pitts.
001450509 264_1 $$aCham :$$bSpringer,$$c[2022]
001450509 264_4 $$c©2022
001450509 300__ $$a1 online resource (viii, 158 pages).
001450509 336__ $$atext$$btxt$$2rdacontent
001450509 337__ $$acomputer$$bc$$2rdamedia
001450509 338__ $$aonline resource$$bcr$$2rdacarrier
001450509 4901_ $$aLecture notes in mathematics ;$$vvolume 2306
001450509 504__ $$aIncludes bibliographical references and indexes.
001450509 5050_ $$aIntro -- Abstract -- Contents -- 1 Introduction -- 2 Inclusions -- 2.1 Local Modules -- 2.2 Regular Ideals and the Localizing Projection -- 2.3 Regular Inclusions -- 2.4 Invariant Ideals -- 2.5 Extended Multiplication for Normalizers -- 2.6 Regularity of Maximal Ideals in Regular Inclusions -- 2.7 Extension of Pure States, Relative Free Points and Smooth Normalizers -- 2.8 Free Points -- 2.9 Fourier Coefficients -- 2.10 Opaque and Gray Ideals -- 2.11 Topologically Free Inclusions -- 2.12 Pseudo-Expectations -- 3 Groupoids -- 3.1 Étale Groupoids -- 3.2 Twists and Line Bundles
001450509 5058_ $$a3.3 The C*-Algebra of a Twisted Groupoid -- 3.4 Topologically Free Groupoids -- 3.5 The Essential Groupoid C*-Algebra -- 3.6 Kwasniewski and Meyer's Version of the Essential Groupoid C*-Algebra -- 3.7 The Relative Weyl Groupoid -- 3.8 Fell Bundles Over Inverse Semigroups -- 3.9 Topological Freeness of the Weyl Groupoidand the Main Theorem -- 3.10 Semi-Masas -- 3.11 Canonical States -- 4 Examples and Open Questions -- 4.1 Example: Non-Smooth Normalizers -- 4.2 Example: Periodic Functions on the Interval -- 4.3 Example: The Gray Ideal of Twisted Groupoid C*-Algebras -- 4.4 Some Open Questions
001450509 5058_ $$a5 Appendix: Isotropy Projection -- References -- Symbol Index -- Concept Index
001450509 506__ $$aAccess limited to authorized users.
001450509 520__ $$aThis book develops tools to handle C*-algebras arising as completions of convolution algebras of sections of line bundles over possibly non-Hausdorff groupoids. A fundamental result of Gelfand describes commutative C*-algebras as continuous functions on locally compact Hausdorff spaces. Kumjian, and later Renault, showed that Gelfand's result can be extended to include non-commutative C*-algebras containing a commutative C*-algebra. In their setting, the C*-algebras in question may be described as the completion of convolution algebras of functions on twisted Hausdorff groupoids with respect to a certain norm. However, there are many natural settings in which the KumjianRenault theory does not apply, in part because the groupoids which arise are not Hausdorff. In fact, non-Hausdorff groupoids have been a source of surprising counterexamples and technical difficulties for decades. Including numerous illustrative examples, this book extends the KumjianRenault theory to a much broader class of C*-algebras. This work will be of interest to researchers and graduate students in the area of groupoid C*-algebras, the interface between dynamical systems and C*-algebras, and related fields.
001450509 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed November 1, 2022).
001450509 650_0 $$aC*-algebras.
001450509 650_0 $$aGroupoids.
001450509 655_0 $$aElectronic books.
001450509 7001_ $$aPitts, David Ryder,$$eauthor.
001450509 77608 $$iPrint version: $$z3031055128$$z9783031055126$$w(OCoLC)1309865554
001450509 830_0 $$aLecture notes in mathematics (Springer-Verlag) ;$$v2306.
001450509 852__ $$bebk
001450509 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-05513-3$$zOnline Access$$91397441.1
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001450509 980__ $$aBIB
001450509 980__ $$aEBOOK
001450509 982__ $$aEbook
001450509 983__ $$aOnline
001450509 994__ $$a92$$bISE