Uniformly Hyperfinite Algebra
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In operator algebras, a uniformly hyperfinite, or UHF, algebra is one that is the closure, in the appropriate topology, of an increasing union of finite dimensional full matrix algebras. A UHF C -algebra is the direct limit of an inductive system {An, n} where each An is a finite dimensional full matrix algebra and each n : An An+1 is a unital embedding. Suppressing the connecting maps, one can write A = overline {cup_n A_n}. If A_n simeq M_{k_n} (mathbb C), then r kn...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In operator algebras, a uniformly hyperfinite, or UHF, algebra is one that is the closure, in the appropriate topology, of an increasing union of finite dimensional full matrix algebras. A UHF C -algebra is the direct limit of an inductive system {An, n} where each An is a finite dimensional full matrix algebra and each n : An An+1 is a unital embedding. Suppressing the connecting maps, one can write A = overline {cup_n A_n}. If A_n simeq M_{k_n} (mathbb C), then r kn = kn + 1 for some integer r and phi_n (a) = a otimes I_r, where Ir is the identity in the r × r matrices. The sequence ...kn kn + 1 kn + 2... determines a formal product, delta(A) = prod_p p^{t_p}, where each p is prime and tp = sup {m pm divides kn for some n}, possibly zero or infinite.
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