论文标题
抛物线代数重新审视
The parabolic algebra revisited
论文作者
论文摘要
抛物线代数A_P是由正确翻译的单一半群产生的l^2（r）的弱封闭的代数，通过分析指数函数e^{iλx}，λ\ geq 0。 （Katavolos and Power，1997）。此识别在这里用于对部分Weyl换向关系的强烈不可还原的等距表示进行分类。合成子空间晶格的概念从交换性晶格延伸到非交通晶格，这表明LAT A_P相对于A_P的最大Abelian乘法亚代理是非合成的。同样，从A_P的等距表示和紧凑的扰动定义和确定的算法代数。
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.
