Cyclic homology, tight crossed products, and small stabilizations

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In [1] we associated an algebra (Formula presented.) to every bornological algebra (Formula presented.) and an ideal (Formula presented.) to every symmetric ideal (Formula presented.). We showed that (Formula presented.) has K-theoretical properties which are similar to those of the usual stabilizat...

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Autor principal: Cortiñas, G.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: European Mathematical Society Publishing House 2014
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Biblioteca Central Dr. Luis F. Leloir (FCEN) de Universidad de Buenos Aires
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024 7 |2 scopus  |a 2-s2.0-84922335286 
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100 1 |a Cortiñas, G. 
245 1 0 |a Cyclic homology, tight crossed products, and small stabilizations 
260 |b European Mathematical Society Publishing House  |c 2014 
506 |2 openaire  |e Política editorial 
504 |a Abadie, B., Cortiñas, G., Homotopy invariance through small stabilizations (2013) Journal of Homotopy and Related Structures, pp. 1-35 
504 |a Buss, A., Exel, R., Fell bundles over inverse semigroups and twisted étale groupoids (2012) J. Operator Theory, 67 (1), pp. 153-205. , Zbl 1249.46053 MR 2881538 
504 |a Calkin, J.W., Two-sided ideals and congruences in the ring of bounded operators in Hilbert space (1941) Ann. of Math. (2), 42, pp. 839-873. , Zbl 0063.00692 MR 5790 
504 |a Cartan, H., Eilenberg, S., (1956) Homological Algebra, , Princeton University Press, Princeton, N. J., Zbl 0075.24305 MR 77480 
504 |a Cohn, P.M., Some remarks on the invariant basis property (1966) Topology, 5, pp. 215-228. , Zbl 0147.28802 MR 197511 
504 |a Cortiñas, G., Algebraic v. topological K-theory: A friendly match (2011) Topics in Algebraic and Topological K-Theory, Lecture Notes in Math., 2008, pp. 103-165. , Springer, Berlin, Zbl 1216.19002 MR 2762555 
504 |a Cortiñas, G., Guccione, J.A., Guccione, J.J., Decomposition of Hochschild and cyclic homology of commutative differential graded algebras (1992) J. of Pure and Appl. Alg., 83, pp. 219-235. , Zbl 0771.13006 MR 1194838 
504 |a Cortiñas, G., Thom, A., Bivariant algebraic K-theory (2007) J. Reine Angew. Math., 610, pp. 71-123. , Zbl 1152.19002 MR 2359851 
504 |a Cortiñas, G., Thom, A., Comparison between algebraic and topological K-theory of locally convex algebras (2008) Adv. Math., 218 (1), pp. 266-307. , Zbl 1142.19002 MR 2409415 
504 |a Cortiñas, G., Thom, A., Algebraic geometry of topological spaces I (2012) Acta Math., 209 (1), pp. 83-131. , Zbl 1266.19003 MR 2979510 
504 |a Cortiñas, G., Weibel, C., Relative Chern characters for nilpotent ideals (2009) Algebraic Topology, Abel Symp., 4, pp. 61-82. , Springer, Berlin, Zbl 05645847 MR 2597735 
504 |a Cuntz, J., Meyer, R., Rosenberg, J.M., Topological and bivariant K-theory (2007) Oberwolfach Seminars, 36. , Birkhäuser Verlag, Basel, Zbl 1139.19001 MR 2340673 
504 |a Dykema, K., Figiel, T., Weiss, G., Wodzicki, M., Commutator structure of operator ideals (2004) Adv. Math., 185 (1), pp. 1-79. , Zbl 1103.47054 MR 2058779 
504 |a Exel, R., Inverse semigroups and combinatorial C∗-algebras (2008) Bull. Braz. Math. Soc. (N.S.), 39 (2), pp. 191-313. , Zbl 1173.46035 MR 2419901 
504 |a Garling, D.J.H., On ideals of operators in Hilbert space (1967) Proc. London Math. Soc. (3), 17, pp. 115-138. , Zbl 0149.34202 MR 208398 
504 |a Khalkhali, M., Rangipour, B., On the generalized cyclic Eilenberg-Zilber theorem (2004) Canad. Math. Bull., 47 (1), pp. 38-48. , Zbl 1048.19004 MR 2032267 
504 |a Loday, J.-L., Cyclic homology (1998) Grundlehren der Mathematischen Wissenschaften, 301. , 2nd ed., Springer-Verlag, Berlin, Zbl 0885.18007 MR 1600246 
504 |a Lück, W., Hilbert modules and modules over finite von Neumann algebras and applications to L2-invariants (1997) Math. Ann, 309, pp. 247-285. , Zbl 0886.57028 MR 1474192 
504 |a Quillen, D., Cyclic cohomology and algebra extensions (1989) K-Theory, 3 (3), pp. 205-246. , Zbl 0696.16021 MR 1040400 
504 |a Suslin, A.A., Wodzicki, M., Excision in algebraic K-theory (1992) Ann. of Math. (2), 136 (1), pp. 51-122. , Zbl 0756.18008 MR 1173926 
504 |a Vigué-Poirrier, M., Décompositions de l'homologie cyclique des algèbres diférentielles graduées commutatives (1991) K-Theory, 4 (5), pp. 399-410. , Zbl 0731.19004 MR 1116926 
504 |a Weibel, C.A., An introduction to homological algebra (1994) Cambridge Studies in Advanced Mathematics, 38. , Cambridge University Press, Cambridge, Zbl 1269324 MR 1269324 
504 |a Wodzicki, M., Excision in cyclic homology and in rational algebraic K-theory (1989) Ann. of Math. (2), 129 (3), pp. 591-639. , Zbl 0689.16013 MR 997314 
504 |a Wodzicki, M., Algebraic K-theory and functional analysis (1994) Progr. Math., 120, pp. 485-496. , First European Congress of Mathematics, Vol. II (Paris, 1992), Birkhäuser, Basel, Zbl 0842.46047 MR 1341858 
520 3 |a In [1] we associated an algebra (Formula presented.) to every bornological algebra (Formula presented.) and an ideal (Formula presented.) to every symmetric ideal (Formula presented.). We showed that (Formula presented.) has K-theoretical properties which are similar to those of the usual stabilization with respect to the ideal (Formula presented) of the algebra β of bounded operators in Hilbert space which corresponds to S under Calkin's correspondence. In the current article we compute the relative cyclic homology (Formula presented.). Using these calculations, and the results of loc. cit., we prove that if (Formula presented) is a C∗-algebra and c0 the symmetric ideal of sequences vanishing at infinity, then (Formula presented.) is homotopy invariant, and that if ∗≥ 0, it contains (Formula presented.) as a direct summand. This is a weak analogue of the Suslin-Wodzicki theorem ([20]) that says that for the ideal Κ = Jc0 of compact operators and the C∗-algebra tensor product (Formula presented.), we have (Formula presented.). Similarly, we prove that if (Formula presented.) is a unital Banach algebra and (Formula presented.), then (Formula presented.) is invariant under Hölder continuous homotopies, and that for ∗≥ 0 it contains (Formula presented.) as a direct summand. These K-theoretic results are obtained from cyclic homology computations. We also compute the relative cyclic homology groups (Formula presented.) in terms of (Formula presented.) for general (Formula presented.) and S. For (Formula presented.) = ℂ and general S, we further compute the latter groups in terms of algebraic differential forms. We prove that the map (Formula presented.) is an isomorphism in many cases. © European Mathematical Society  |l eng 
536 |a Detalles de la financiación: Ministerio de Ciencia, Tecnología e Innovación Productiva, MINCyT 
593 |a Department of Matemática-IMAS, FCEyN-UBA, Ciudad Universitaria Pab 1, Buenos Aires, 1428, Argentina 
690 1 0 |a CALKIN'S THEOREM 
690 1 0 |a CROSSED PRODUCT 
690 1 0 |a CYCLIC HOMOLOGY 
690 1 0 |a KAROUBI'S CONE 
690 1 0 |a OPERATOR IDEAL 
773 0 |d European Mathematical Society Publishing House, 2014  |g v. 8  |h pp. 1191-1223  |k n. 4  |p J. Noncommunitative Geom.  |x 16616952  |t Journal of Noncommutative Geometry 
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856 4 0 |u https://doi.org/10.4171/JNCG/184  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_16616952_v8_n4_p1191_Cortinas  |y Handle 
856 4 0 |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16616952_v8_n4_p1191_Cortinas  |y Registro en la Biblioteca Digital 
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