Abstract
In this article we consider the Ore extension algebra for the algebra \(\mathcal {A}\) of functions with finite support on a countable set. We derive explicit formulas for twisted derivations on \(\mathcal {A},\) give a description for the centralizer of \(\mathcal {A},\) and the center of the Ore extension algebra under specific conditions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Archbold, R.J., Spielberg, J. S.: Topologically free actions and ideals in descrete C*-dynamical systems. Proc. Edinb. Math. Soc. (2) 37(1), 119–124 (1994)
Carlsen, T.M., Silvestrov, S.: On the Exel crossed product of topological covering maps. Acta Appl. Math. 108(3), 573–583 (2009)
de Jeu, M., Svensson, C., Tomiyama, J.: On the Banach *-algebra crossed product associated with a topological dynamical system. J. Funct. Anal. 262(11), 4746–4765 (2012)
Dutkay, D.E., Jorgensen, P.E.T., Silvestrov, S.: Decomposition of wavelet representations and Martin boundaries. J. Funct. Anal. 262(3), 1043–1061 (2012)
Dutkay, D.E., Jorgensen, P.E.T.: Martingales, endomorphisms and covariant systems of operators in Hilbert space. J. Oper. Theory Anal. 58(2), 269–310 (2007)
Exel, R., Vershik, A.: C*-algebras of irreversible dynamical systems. Canad. J. Math. 58(1), 39–63 (2006)
Goodearl, K.R., Warfield, R.B.: An introduction to non commutative Noetherian rings. London Mathematical Society Student Texts, vol. 61, 2nd edn. Cambridge University Press, Cambridge (2004)
Li, B.-R.: Introduction to Operator Algebras. World Science, Singapore (1992)
Lundström, P., Öinert, J.: Skew category algebras associated with partially defined dynamical systems. Int. J. Math. 23(4), 16 (2012)
Mackey, G.W.: Unitary Group Representations in Physics, Probability and Number Theory, 2nd edn., xxviii+402pp. Advanced book classics. Addison-Wesley Publishing Company, Advanced Book Program, Redwood city (1989)
Ostrovskyĭ, V., Samoĭlenko, Yu.: Introducion to the Theory of Representations of Finitely Presented *-Algebras, I, iv+261 pp. Representations by bounded operators. Reviews in Mathematics and Mathematical Physics, vol. 11, pt.1. Harwood Academic Publishers, Amsterdam (1999)
Öinert, J., Silvestrov, S.D.: Commutativity and ideals in algebraic crossed products. J. Gen. Lie Theory Appl. 2(4), 287–302 (2008)
Öinert, J., Silvestrov, S.D.: Commutativity and ideals in pre-crystalline graded rings. Acta Appl. Math. 108(3), 603–615 (2009)
Öinert, J., Richter, J., Silvestrov, S.D.: Maximal commutative subrings and simplicity in Ore extensions. J. Algebra Appl. 12, 1250192 (2013)
Richter, J., Silvestrov, S., Tumwesigye, B.A.: Commutants in crossed product algebras for piece-wise constant functions. In: Silvestrov, S., Rančić, M. (eds.), Engineering Mathematics II, Springer Proceedings in Mathematics and Statistics, vol. 179, 95–108. Springer, Cham (2016)
Richter, J., Silvestrov, S., Ssembatya, V.A., Tumwesigye, A.B.: Crossed product algebras for piece-wise constant functions. In: Silvestrov, S., Rančić, M., (eds.), Engineering Mathematics II, Springer Proceedings in Mathematics and Statistics, vol. 179, 75–93. Springer, Cham (2016)
Richter, J.: Centralizers and pseudo-degree functions. In: Silvestrov, S., Rančić, M. (eds.) Engineering Mathematics II. Springer Proceedings in Mathematics and Statistics, vol 179, 65–73. Springer, Cham (2016)
Richter, J., Silvestrov, S.: Centralizers in Ore extensions of polynomial rings. Int. Electron. J. Algebra 15, 196–207 (2014)
Rowen, L.H.: Ring theory. Pure and Applied Mathematics, vol. I, p. 127. Academic Press, Inc., Boston, MA (1988)
Svensson, C., Silvestrov, S., de Jeu, M.: Dynamical systems associated with crossed products. Acta Appl. Math. 108(3), 547–559 (2009)
Svensson, C., Silvestrov, S., de Jeu, M.: Dynamical systems and commutants in crossed products. Int. J. Math. 18(4), 455–471 (2007)
Tomiyama, J.: Invitation to \(C^*-\)Algebras and Topological Dynamics. World Science, Singapore, NJ, Hong Kong (1987)
Acknowledgements
This research was supported by the Swedish International Development Cooperation Agency (Sida) and International Science Programme (ISP) in Mathematical Sciences (IPMS), Eastern Africa Universities Mathematics Programme (EAUMP). Alex Behakanira Tumwesigye is also grateful to the research environment Mathematics and Applied Mathematics (MAM), Division of Applied Mathematics, Mälardalen University for providing an excellent and inspiring environment for research education and research.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Tumwesigye, A.B., Richter, J., Silvestrov, S. (2020). Ore Extensions of Function Algebras. In: Silvestrov, S., Malyarenko, A., Rančić, M. (eds) Algebraic Structures and Applications. SPAS 2017. Springer Proceedings in Mathematics & Statistics, vol 317. Springer, Cham. https://doi.org/10.1007/978-3-030-41850-2_19
Download citation
DOI: https://doi.org/10.1007/978-3-030-41850-2_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-41849-6
Online ISBN: 978-3-030-41850-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)