On Permutative Representations of O(subscript N)

在庫玆代數上之交換表示

黃苑青(Yuan-Ching Huang)

《育達學院學報》 9期 (2005/03) Pp. 283-290

https://doi.org/10.7074/YDAJ.200503.0283

摘要

令π是一個作用在希爾伯特空間H上，相對於一組可數的單位正交基底(orthonormal basis)β＝｛e(下標 n)｝(下標 n∈N)之m次庫玆代數O(下標 m)(Cuntz algebra of order m)之交換表示(permutative representation)，且κ⊂O(下標 m)(e(下標 n))是π的一個不變子空間(invariant subspace)。我們証明了若κ擁有一組相對於基底β之減縮基底(reduced basis)，則O(下標 m)(e(下標 n))有一個週期(period)。

並列摘要

Let π be a permutation representation of O(subscript N) on a Hilbert space κ with respect to an orthonormal basis β=｛e(subscript n)｝(subscript n∈N) and κ∈O(subscript N)(e(subscript n)) be a proper invariant (under π) subspace. We show that if κ has a reduced basis with respect to β, then O(subscript N)(e(subscript n)) has a period.