齐次 C* - 代数之间同态的阻碍
Obstructions to homomorphisms between homogeneous C*-algebras
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中文总结 AI 辅助
开发方法找齐次C* - 代数间同态存在的新阻碍，回答Blackadar 1993年关于偶数维球面上矩阵值函数代数间单位同态在\(K_0\)单射存在性问题，给出特定条件下不存在此类同态的结论。
中文摘要 AI 辅助
我们开发了一种方法，用于找到齐次 C* - 代数之间同态存在的新阻碍，该同态在 K - 理论上具有规定行为。作为应用，我们完整回答了Blackadar在1993年提出的一个问题，该问题涉及偶数维球面上矩阵值函数代数之间单位同态在\(K_0\)上是单射的存在性。我们证明，如果\(n\)、\(d\)、\(k\)、\(r\)是自然数且\(k\)不在\(n, n + 1, \cdots, n + d - 1\)范围内，那么从\(C(S^{2n}, M_r)\)到\(C(S^{2k}, M_{dr})\)不存在在\(K_0\)上是单射的单位同态。
英文摘要
We develop a method to find new obstructions to the existence of homomorphisms between homogeneous C*-algebras with prescribed behavior on K-theory. As an application, we give a complete answer to a problem posed by Blackadar in 1993 concerning the existence of unital homomorphisms between algebras of matrix-valued functions on even spheres which are injective on K_0: we show that if n, d, k, r are natural numbers and k is not in the range n, n+1, ..., n+d-1, then there is no unital homomorphism from C (S^{2n}, M_r) to C (S^{2k}, M_{dr}) which is injective on K_0.
