000 | 03177nam a22004575i 4500 | ||
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001 | 978-3-540-47868-3 | ||
003 | DE-He213 | ||
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007 | cr nn 008mamaa | ||
008 | 121227s1987 gw | s |||| 0|eng d | ||
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_a9783540478683 _9978-3-540-47868-3 |
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024 | 7 |
_a10.1007/BFb0078657 _2doi |
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_aPBPD _2bicssc |
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_aMAT038000 _2bisacsh |
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_aPBPD _2thema |
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082 | 0 | 4 |
_a514.2 _223 |
100 | 1 |
_aPhillips, N. Christopher. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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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. |
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300 |
_aX, 374 p. _bonline resource. |
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_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1274 |
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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 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0078657 |
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