抛物代数再论
The parabolic algebra revisited
摘要：
抛物代数A_p是L^2（R）上由右平移酉半群和解析指数函数e^{iλx}，λ \geq 0乘酉半群生成的弱闭代数.这个代数是自反的，有一个不变子空间格Lat A_p，它自然地同胚于单位圆盘（Katavolos and Power，1997）。这种识别在这里被用来分类强不可约等距表示的部分外尔交换关系。将合成子空间格的概念从交换格推广到非交换格，证明了Lat A_p相对于A_p的极大交换乘法子代数是非合成的，并定义和确定了由A_p的等距表示和紧扰动导出的算子代数.
英文摘要：
The parabolic algebra A_p is the weakly closed algebra on L^2(R) generated by the unitary semigroup of right translations and the unitary semigroup of multiplication by the analytic exponential functions e^{iλx}, λ\geq 0. This algebra is reflexive with an invariant subspace lattice, Lat A_p, which is naturally homeomorphic to the unit disc (Katavolos and Power, 1997). This identification is used here to classify strongly irreducible isometric representations of the partial Weyl commutation relations. The notion of a synthetic subspace lattice is extended from commutative to noncommutative lattices and it is shown that Lat A_p is nonsynthetic relative to the maximal abelian multiplication subalgebra of A_p. Also, operator algebras derived from isometric representations of A_p and from compact perturbations are defined and determined.
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