Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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HOMOGENEOUS $C^*$-ALGEBRAS OVER A SPHERE

  • Park, Chun-Gil (Department of Mathematics Chungnam National University )
  • Published : 1997.11.01
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Abstract

It is shown that for $A_{k, m}$ a k-homogeneous $C^*$-algebra over $S^{2n - 1} \times S^1$ such that no non-trivial matrix algebra can be factored out of $A_{k, m}$ and $A_{k, m} \otimes M_l(C)$ has a non-trivial bundle structure for any positive integer l, we construct an $A_{k, m^-} C(S^{2n - 1} \times S^1) \otimes M_k(C)$-equivalence bimodule to show that every k-homogeneous $C^*$-algebra over $S^{2n - 1} \times S^1)$. Moreover, we prove that the tensor product of the k-homogeneous $C^*$-algebra $A_{k, m}$ with a UHF-algebra of type $p^\infty$ has the tribial bundle structure if and only if the set of prime factors of k is a subset of the set of prime factors of pp.

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References

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