Skip to main content
SpringerLink
Log in

On compact quantum semigroup QS red

  • Brief Communications
  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We study some properties of a reduced semigroup C*-algebra of a semigroup S. For the semigroup C*-algebra generated by the deformation of the algebra of continuous functions on a compact abelian group we obtain a structure of a compact quantum semigroup. We also consider morphisms of constructed compact quantum semigroups.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. V. G. Drinfeld, “Quantum Groups,” in Proceedings of International Congress of Mathematicians, Berkeley, 1986 (Providence, RI, Amer. Math. Soc., 1987), pp. 798–820.

    Google Scholar 

  2. S. L. Woronowicz, “Twisted SU(2)-Group: An Example of Non-Commutative Differential Calculus,” Publ. Res. Inst. Math. Sci. 23, 117–181 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  3. N. Yu. Reshetikhin, L. A. Takhtadzhyan, and L.D. Faddeev, “Quantization of Lie Groups and Lie Algebras,” Algebra i Analiz 1(1), 178–206 (1989).

    MathSciNet  Google Scholar 

  4. A. Maes and A. Van Daele, “Notes on Compact Quantum Groups,” Nieuw Arch. Wisk. 4(16), 73–112 (1998).

    Google Scholar 

  5. M. A. Aukhadiev, S. A. Grigoryan, and E. V. Lipacheva, “Infinite-Dimensional Compact Quantum Semigroup,” Lobachevskii J. Math. 32(4), 304–316 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  6. K. Kawamura, “C*-Bialgebra Defined by the Direct Sum of Cuntz Algebras,” J. Algebra 319, 3935–3959 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  7. S. A. Grigoryan and A. F. Salakhutdinov, “C*-Algebras Generated by Semigroups,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 10, 68–71 (2009) [Russian Mathematics (Iz. VUZ) 53 (10), 61–63 (2009)]

    Google Scholar 

  8. S. A. Grigoryan and A. F. Salakhutdinov, “C*-Algebras Generated by Cancellative Semigroups,” Sib. Matem. Zhurn. 51(1), 16–25 (2010).

    MathSciNet  Google Scholar 

  9. M. A. Aukhadiev and V. H. Tepoyan, “Isometric Representations of Totally Ordered Semigroups,” Lobachevskii J. Math. 33(3), 239–243 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  10. S. L. Woronowicz, “Compact Quantum Groups,” in Proceedings of the Les Houches Summer School, Session LXIV, Les Houches, France, August 1–September 8, 1995 (North-Holland, Amsterdam, 1998), p. 845–884.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kazan State Power Engineering University, ul. Krasnosel’skaya 51, Kazan, 420066, Russia

    M. A. Aukhadiev, S. A. Grigoryan & E. V. Lipacheva

Authors
  1. M. A. Aukhadiev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. A. Grigoryan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. V. Lipacheva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. A. Aukhadiev.

Additional information

Original Russian Text © M.A. Aukhadiev, S.A. Grigoryan, and E.V. Lipacheva, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 10, pp. 55–62.

Submitted by D.Kh. Mushtari

About this article

Cite this article

Aukhadiev, M.A., Grigoryan, S.A. & Lipacheva, E.V. On compact quantum semigroup QS red . Russ Math. 57, 54–58 (2013). https://doi.org/10.3103/S1066369X1310006X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X1310006X

Keywords and phrases

Search

Navigation