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The Structure of some C*-Algebras Generated by N Idempotents

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Recent Advances in Operator Theory, Operator Algebras, and their Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 153))

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Abstract

We study the structure of some n-homogeneous C*-algebras generated by flips. The algebra is generated by the flips u, v, s1, …, sm with the relations between the generators: usi = αisiu, vs i = βisiv, sisj = Єijsjsi, αi = ±1, βi = ±1, ij = ±1, 1 ≤ i, j ≤ m. The structure of such algebras generated by flips with the relations between generators was studied by Popovich, Samoilenko and Turowska. In the paper we prove that if such an algebra A is n-homogeneous then it is trivial. Such an n-homogeneous C*-algebra A is isomorphic to the algebra of all continuous matrix-functions of dimension n over some compact subspace of the plane ℂ.

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Authors and Affiliations

  1. Department of Functional Analysis, Belarusian State University, Scoriny av. 4, Minsk, Belarus

    Mikhail Shchukin & Elena Vatkina

Authors
  1. Mikhail Shchukin
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  2. Elena Vatkina
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of the West Timişoara, Bul. V. Parvan Nr. 4, 1900, Timişoara, Romania

    Dumitru Gaşpar

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest, 70700, Romania

    Dan Timotin

  3. Dipartimento di Matematica, Università di Roma „Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Roma, Italy

    László Zsidó

  4. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    Israel Gohberg

  5. Laboratoire AGAT-UMR 8524 U.F.R. de mathématiques, Université des Sciences et Technologie de Lille, 59655, Villeneuve d’Ascq Cedex, France

    Florian-Horia Vasilescu

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© 2004 Birkhäuser Verlag Basel/Switzerland

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Shchukin, M., Vatkina, E. (2004). The Structure of some C*-Algebras Generated by N Idempotents. In: Gaşpar, D., Timotin, D., Zsidó, L., Gohberg, I., Vasilescu, FH. (eds) Recent Advances in Operator Theory, Operator Algebras, and their Applications. Operator Theory: Advances and Applications, vol 153. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7314-8_15

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