1. Andrzej Sitarz
On the geometry of kappa-deformation
International Journal of Geometric Methods in Modern Physics, vol. 9, pp. 1261011-1261021 (2012).
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Abstract:
We present a brief outline of recent and new results on the mathematical structure underlying the kappa-deformed space. We suggest to turn attention to the observable C*-algebra of kappa-deformed coordinates and its Galilean symmetries. *supported by the grant from The John Templeton Foundation

2. P. Olczykowski, A.Sitarz
K-theory of noncommutative Bieberbach manifolds,
(2012).
[abstract] [preprint]

Abstract:
We compute K-theory of noncommutative Bieberbach manifolds, which quotients of a three-dimensional noncommutative torus by a free action of a cyclic group Z_N, N = 2; 3; 4; 6.

3. A. Sitarz, A. Zając
Spectral action for scalar perturbations of Dirac operators
Lett. Math. Phys., vol. 98, pp. 333-348 (2011).
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Abstract:
We investigate the leading terms of the spectral action for odd-dimensional Riemannian spin manifolds with the Dirac operator perturbed by a scalar function. We calculate first two Gilkey–de Witt coefficients and make explicit calculations for the case of n-spheres with a completely symmetric Dirac. In the special case of dimension 3, when such perturbation corresponds to the completely antisymmetric torsion, we carry out the noncommutative calculation following Chamseddine and Connes (J Geom Phys 57:121, 2006) and study the case of SU q (2).

4. B. Iochum, T. Masson, T. Schücker, A. Sitarz
Compact kappa-deformation and spectral triples
Rep. Math. Phys., vol. 68, pp. 37-64 (2011).
[abstract] [journal]

Abstract:
We construct discrete versions of κ-Minkowski space related to a certain compactness of the time coordinate. We show that these models fit into the framework of noncommutative geometry in the sense of spectral triples. The dynamical system of the underlying discrete groups (which include some Baumslag–Solitar groups) is heavily used in order to construct finitely summable spectral triples. This allows to bypass an obstruction to finite-summability appearing when using the common regular representation. The dimension of these spectral triples is unrelated to the number of coordinates defining the κ-deformed Minkowski spaces.

5. B. Iochum, T. Masson, T. Schücker, A. Sitarz
Kappa-deformation and Spectral Triples
Acta Phys. Polon. Supp., vol. 4, p. 305 (2011).
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Abstract:
The aim of the paper is to answer the following question: does kappa -deformation fit into the framework of noncommutative geometry in the sense of spectral triples? Using a compactification of time, we get a discrete version of kappa -Minkowski deformation via C*-algebras of groups. The dynamical system of the underlying groups (including some Baumslag–Solitar groups) is used in order to construct finitely summable spectral triples. This allows to bypass an obstruction to finite-summability appearing when using the common regular representation.

6. P. Olczykowski, A. Sitarz
On spectral action over Bieberbach manifolds
Acta Phys. Pol., B , vol. 42, p. 1189 (2011).
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Abstract:
We compute the leading terms of the spectral action for orientable three dimensional Bieberbach manifolds using two different methods: the Poisson summation formula and the perturbative expansion. Assuming that the cut-off function is not necessarily symmetric we find that the scale invariant part of the perturbative expansion might only differ from the spectral action of the flat three-torus by the value of the eta invariant.