2-Homogeneous C*-algebras with the space of primitive ideals homeomorphic to a two-dimensional oriented compact connected manifold generated by idempotents

Authors

  • Mikhail V. Shchukin Belarusian National Technical University, 65 Niezaliežnasci Avenue, Minsk 220013, Belarus

Keywords:

C*-algebra, idempotent, finite-dimensional irreducible representations, operator algebras, number of gene rators

Abstract

Before showed in 1961 that every n-homogeneous C*-algebra is isomorphic to the algebra of all continuous sections for the appropriate algebraic bundle. The base space for the bundle is homeomorphic to the space of primitive ideals for the algebra in the appropriate topology. By using that we considered the 2-homogeneous C*-algebra A such that the space of primitive ideals of the algebra is homeomorphic to a two-dimensional compact oriented connected manifold. We constructed three idempotents from the algebra A that generated the algebra.

Author Biography

  • Mikhail V. Shchukin, Belarusian National Technical University, 65 Niezaliežnasci Avenue, Minsk 220013, Belarus

    PhD (physics and mathematics), docent; associate professor at the department of higher mathematics No. 1, faculty of information technology and robotics

References

  1. Bottcher A., Gohberg I., Karlovich Yu., et al. Banach algebras generated by N idempotents and applications. Oper. Theory. Adv., Appl. 1996. Vol. 90. P. 19–54. DOI: 10.1007/978-3-0348-9040-3_2.
  2. Antonevich A., Krupnik N. On trivial and non-trivial n-homogeneous C*-algebras. Integr. Equ. Oper. Theory. 2000. Vol. 38, issue 2. P. 172–189. DOI: 10.1007/BF01200122.
  3. Shchukin M. V. [Non-trivial C*-algebra generated by four idempotents]. Proc. of the Inst. of Math. of the Natl. Acad. of Sci. of Belarus. 2001. Vol. 9. P. 161–163 (in Russ.).
  4. Shchukin M. Non-trivial C*-algebras generated by idempotents. Proceedings of the International Conference on Nonlinear Ope rators, Differential Equations and Applications : semin. on fixed point theory Cluj-Napoca : in 3 vols (Cluj-Napoca, 12–17 Sept., 2001). Cluj-Napoca, 2002. Vol. 3. P. 353–359.
  5. Krupnik N., Roch S., Silbermann B. On C*-algebras generated by idempotents. J. Funct. Anal. 1996. Vol. 137, issue 2. P. 303–319. DOI: 10.1006/jfan.1996.0048.
  6. Rabanovich V. I. [The matrix algebras and the theory of representations] : diss. … PhD (phys. and math.) : 01.01.01. Kiev, 2000 (in Ukrainian).
  7. Shchukin M. V. [n-Homogeneous C*-algebras with the set of primitive ideals homeomorphic to an oriented connected compact two-dimensional manifold]. Proc. Natl. Acad. of Sci. of Belarus. Phys. and Math. Ser. 2010. No. 2. P. 12–17 (in Russ.).
  8. Massi U. Algebraicheskaya topologiya. Moscow : Mir, 1977.

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Published

2018-05-05

Issue

No. 1 (2018): Journal of the Belarusian State University. Mathematics and Informatics

Section

Real, Complex and Functional Analysis

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How to Cite

[1]
Shchukin, M.V. 2018. 2-Homogeneous C*-algebras with the space of primitive ideals homeomorphic to a two-dimensional oriented compact connected manifold generated by idempotents. Journal of the Belarusian State University. Mathematics and Informatics. 1 (May 2018), 4–9.