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001 978-3-540-47868-3
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008 121227s1987 gw | s |||| 0|eng d
020 _a9783540478683
_9978-3-540-47868-3
024 7 _a10.1007/BFb0078657
_2doi
050 4 _aQA612-612.8
072 7 _aPBPD
_2bicssc
072 7 _aMAT038000
_2bisacsh
072 7 _aPBPD
_2thema
082 0 4 _a514.2
_223
100 1 _aPhillips, N. Christopher.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aEquivariant K-Theory and Freeness of Group Actions on C*-Algebras
_h[electronic resource] /
_cby N. Christopher Phillips.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1987.
300 _aX, 374 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1274
505 0 _aIntroduction: The commutative case -- Equivariant K-theory of C*-algebras -- to equivariant KK-theory -- Basic properties of K-freeness -- Subgroups -- Tensor products -- K-freeness, saturation, and the strong connes spectrum -- Type I algebras -- AF algebras.
520 _aFreeness of an action of a compact Lie group on a compact Hausdorff space is equivalent to a simple condition on the corresponding equivariant K-theory. This fact can be regarded as a theorem on actions on a commutative C*-algebra, namely the algebra of continuous complex-valued functions on the space. The successes of "noncommutative topology" suggest that one should try to generalize this result to actions on arbitrary C*-algebras. Lacking an appropriate definition of a free action on a C*-algebra, one is led instead to the study of actions satisfying conditions on equivariant K-theory - in the cases of spaces, simply freeness. The first third of this book is a detailed exposition of equivariant K-theory and KK-theory, assuming only a general knowledge of C*-algebras and some ordinary K-theory. It continues with the author's research on K-theoretic freeness of actions. It is shown that many properties of freeness generalize, while others do not, and that certain forms of K-theoretic freeness are related to other noncommutative measures of freeness, such as the Connes spectrum. The implications of K-theoretic freeness for actions on type I and AF algebras are also examined, and in these cases K-theoretic freeness is characterized analytically.
650 0 _aAlgebraic topology.
650 1 4 _aAlgebraic Topology.
_0http://scigraph.springernature.com/things/product-market-codes/M28019
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662204658
776 0 8 _iPrinted edition:
_z9783540182771
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1274
856 4 0 _uhttps://doi.org/10.1007/BFb0078657
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c12127
_d12127