On С ∗-algebras generated by idempotents

Authors

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

Keywords:

C ∗-algebra, idempotent, finitely generated algebra, number of generators, primitive ideals, base space, algebraic bundle, operator algebra, irreducible representation

Abstract

Banach algebras generated by two idempotents appear in many places. In 1968–1969 P. R. Halmos and G. K. Pedersen studied C ∗-algebras generated by two self-adjoint projections. The Banach algebras generated by two idempotents were described by S. Roch and B. Silbermann in 1988. Such algebras can have irreducible representations of first or second order. The theory of Banach algebras generated by three idempotents has not yet been constructed. Such algebras can have irreducible representations of any order. In 1974 F. Krauss and T. Lawson described the n-homogeneous C ∗-algebras over spheres S 2, S 3, S4. By using these results we prove that n-homogeneous (n > 2) C ∗-algebra such that PrimA = S4 can be generated by finite number of idempotents.

Author Biography

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

    PhD (physics and mathematics), docent; head of the department of high mathematics, faculty of information technology and robotics

     

References

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Published

2023-12-22

Issue

No. 3 (2023): Journal of the Belarusian State University. Mathematics and Informatics

Section

Short Communications

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How to Cite

[1]
Shchukin, M.V. 2023. On С ∗-algebras generated by idempotents. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Dec. 2023), 98–103.