nLab homogeneous C-star-algebra

Redirected from "homogeneous C*-algebra".

Idea

A C*-algebra is called nn-homogeneous (or n-dimensionally homogeneous) if each irreducible C C^\star-representation of the algebra is nn-dimensional.

References

  • Jun Tomiyama, Masamichi Takesaki, Applications of fibre bundles to the certain class of C *C^\ast-algebras, Tohoku Math. J. (2) 13:3 (1961) 498–522 euclid doi

Let AA be a C *{}^\ast-algebra. If the set of pure states of AA is compact and that of primitive ideal?s which are the kernels of one-dimensional irreducible reprentations forms an open set in the structure space of AA, then AA is isomorphic to the C *{}^\ast-sum of a finite number of homogeneous C *{}^\ast-algebras.

  • Shaun Disney, Iain Raeburn, Homogeneous C *{}^\ast-algebras whose spectra are tori, J. Australian Math. Soc. 38:1 (1985) 9–39 doi

The comparison of the Artin’s theorem on characterization of Azumaya algebras and Tomiyama-Takesaki’s theorem on nn-homogeneous C *C^\ast-algebras is in chapter 9 of

  • Edward Formanek, Noncommutative invariant theory, in: Group actions on rings (Brunswick, Maine, 1984), 87–119, Contemp. Math. 43, Amer. Math. Soc. 1985 doi

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