The K-theory ranks for crossed products of C*-algebras by the group of integers
-
Takahiro Sudo
sudo@math.u-ryukyu.ac.jp
Downloads
DOI:
https://doi.org/10.4067/S0719-06462019000300001Abstract
We study the K-theory ranks for crossed products of C∗-algebras by the group of integers. As an application, we obtain certain estimates for the K-theory ranks of the group C∗-algebras of torsion free, finitely generated, nilpotent or solvable discrete groups, written as successive semi-direct products.
Keywords
[1] B. Blackadar, K-theory for Operator Algebras, Second Edition, Cambridge, (1998).
[2] G. K. Pedersen, C∗-Algebras and their Automorphism Groups, Academic Press (1979).
[3] M. Pimsner and D. Voiculescu, Exact sequences for K-groups and Ext-groups of certain cross-product C∗-algebras, J. Operator Theory 4 (1) (1980), 93-118.
[4] Derek J. S. Robinson, A Course in the Theory of Groups, Second Edition, Graduate Texts in Math., 80, Springer (1996).
[5] T. Sudo, K-theory of continuous fields of quantum tori, Nihonkai Math. J. 15 (2004), 141-152.
[6] T. Sudo, K-theory ranks and index for C∗-algebras, Ryukyu Math. J. 20 (2007), 43-123.
[7] T. Sudo, K-theory for the group C∗-algebras of nilpotent discrete groups, Cubo A Math. J.15 (2013), no. 3, 123-132.
[8] T. Sudo, The Euler characteristic and the Euler-Poincar Ìe formula for C∗-algebras, Sci. Math. Japon. 77, No. 1 (2014), 119-138 :e-2013, 621-640.
[9] T. Sudo, The K-theory for the C∗-algebras of nilpotent discrete groups by examples, Bulletin of the Faculty of Science, University of the Ryukyus, No. 104, (September 2017), 1-40.
[10] J. Tomiyama, Invitation to C∗-algebras and topological dynamics, World Scientific (1987).
[11] N. E. Wegge-Olsen, K-theory and C∗-algebras, Oxford Univ. Press (1993).
[2] G. K. Pedersen, C∗-Algebras and their Automorphism Groups, Academic Press (1979).
[3] M. Pimsner and D. Voiculescu, Exact sequences for K-groups and Ext-groups of certain cross-product C∗-algebras, J. Operator Theory 4 (1) (1980), 93-118.
[4] Derek J. S. Robinson, A Course in the Theory of Groups, Second Edition, Graduate Texts in Math., 80, Springer (1996).
[5] T. Sudo, K-theory of continuous fields of quantum tori, Nihonkai Math. J. 15 (2004), 141-152.
[6] T. Sudo, K-theory ranks and index for C∗-algebras, Ryukyu Math. J. 20 (2007), 43-123.
[7] T. Sudo, K-theory for the group C∗-algebras of nilpotent discrete groups, Cubo A Math. J.15 (2013), no. 3, 123-132.
[8] T. Sudo, The Euler characteristic and the Euler-Poincar Ìe formula for C∗-algebras, Sci. Math. Japon. 77, No. 1 (2014), 119-138 :e-2013, 621-640.
[9] T. Sudo, The K-theory for the C∗-algebras of nilpotent discrete groups by examples, Bulletin of the Faculty of Science, University of the Ryukyus, No. 104, (September 2017), 1-40.
[10] J. Tomiyama, Invitation to C∗-algebras and topological dynamics, World Scientific (1987).
[11] N. E. Wegge-Olsen, K-theory and C∗-algebras, Oxford Univ. Press (1993).
Most read articles by the same author(s)
- Takahiro Sudo, K-theory for the C*-algebras of continuous functions on certain homogeneous spaces in semi-simple Lie groups. , CUBO, A Mathematical Journal: Vol. 14 No. 2 (2012): CUBO, A Mathematical Journal
- Takahiro Sudo, K-theory for the group C*-algebras of nilpotent discrete groups , CUBO, A Mathematical Journal: Vol. 15 No. 3 (2013): CUBO, A Mathematical Journal
- Takahiro Sudo, K-theory for the group C*-algebras of a residually finite discrete group with Kazhdan property T , CUBO, A Mathematical Journal: Vol. 16 No. 2 (2014): CUBO, A Mathematical Journal
- Takahiro Sudo, Computing the Laplace transform and the convolution for more functions adjoined , CUBO, A Mathematical Journal: Vol. 17 No. 3 (2015): CUBO, A Mathematical Journal
- Takahiro Sudo, The Flip Crossed Products of the ð¶*-Algebras by Almost Commuting Isometries , CUBO, A Mathematical Journal: Vol. 10 No. 3 (2008): CUBO, A Mathematical Journal
- Takahiro Sudo, Computing the inverse Laplace transform for rational functions vanishing at infinity , CUBO, A Mathematical Journal: Vol. 16 No. 3 (2014): CUBO, A Mathematical Journal
- Takahiro Sudo, Continuous or Discontinuous Deformations of C*-Algebras , CUBO, A Mathematical Journal: Vol. 10 No. 1 (2008): CUBO, A Mathematical Journal
- Takahiro Sudo, Real and stable ranks for certain crossed products of Toeplitz algebras , CUBO, A Mathematical Journal: Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal
- Takahiro Sudo, A covering dimension for ð¶*-algebras , CUBO, A Mathematical Journal: Vol. 8 No. 1 (2006): CUBO, A Mathematical Journal
- Takahiro Sudo, Spectral Rank for ð¶*-Algebras , CUBO, A Mathematical Journal: Vol. 10 No. 2 (2008): CUBO, A Mathematical Journal
Similar Articles
- Youssef N. Raffoul, Ernest Yankson, Positive periodic solutions of functional discrete systems with a parameter , CUBO, A Mathematical Journal: Vol. 21 No. 1 (2019)
- Aymen Ammar, Aref Jeribi, Kamel Mahfoudhi, Generalized trace pseudo-spectrum of matrix pencils , CUBO, A Mathematical Journal: Vol. 21 No. 2 (2019)
- Abdi Oli, Kelelaw Tilahun, G. V. Reddy, The Multivariable Aleph-function involving the Generalized Mellin-Barnes Contour Integrals , CUBO, A Mathematical Journal: Vol. 22 No. 3 (2020)
- Edoardo Ballico, Curves in low dimensional projective spaces with the lowest ranks , CUBO, A Mathematical Journal: Vol. 22 No. 3 (2020)
- Alain Escassut, Idempotents in an ultrametric Banach algebra , CUBO, A Mathematical Journal: Vol. 23 No. 1 (2021)
- Chia-chi Tung, Pier Domenico Lamberti, On Rellich‘s Lemma, the Poincaré inequality, and Friedrichs extension of an operator on complex spaces , CUBO, A Mathematical Journal: Vol. 23 No. 2 (2021)
- M. Haviar, S. Kurtulík, A new class of graceful graphs: \(k\)-enriched fan graphs and their characterisations , CUBO, A Mathematical Journal: Vol. 23 No. 2 (2021)
- Abdelhai Elazzouzi, Khalil Ezzinbi, Mohammed Kriche, On the periodic solutions for some retarded partial differential equations by the use of semi-Fredholm operators , CUBO, A Mathematical Journal: Vol. 23 No. 3 (2021)
- Robert Auffarth, Giancarlo Lucchini Arteche, Pablo Quezada, Smooth quotients of abelian surfaces by finite groups that fix the origin , CUBO, A Mathematical Journal: Vol. 24 No. 1 (2022)
- Hasnae El Hammar, Chakir Allalou, Adil Abbassi, Abderrazak Kassidi, The topological degree methods for the fractional \(p(\cdot)\)-Laplacian problems with discontinuous nonlinearities , CUBO, A Mathematical Journal: Vol. 24 No. 1 (2022)
<< < 17 18 19 20 21 22 23 24 25 26 > >>
You may also start an advanced similarity search for this article.
Downloads
Download data is not yet available.
Published
2020-01-08
How to Cite
[1]
T. Sudo, “The K-theory ranks for crossed products of C*-algebras by the group of integers”, CUBO, vol. 21, no. 3, pp. 01–08, Jan. 2020.
Issue
Section
Articles
