The K-theory ranks for crossed products of C*-algebras by the group of integers
DOI:
https://doi.org/10.4067/S0719-06462019000300001Keywords:
K-theory, C*-algebra, crossed product, Betti number, discrete groupAbstract
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.
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References
[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).
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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.
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