C*-乘子、交叉积代数和正则对易关系
C*-Multipliers, crossed product algebras, and canonical commutation relations
摘要：
群X的乘子的概念通过允许它在任意C*-代数A中取值而推广到C*-乘子的概念。另一方面，X在A中的作用的概念被推广到X的投射作用作为在X中具有紧支集且在A中具有值的连续函数空间的线性变换的概念。证明了C*-乘子与投射作用之间存在一一对应关系。C*-乘子被用来定义扭群代数。另一方面，投射作用τ可以用来构造交叉积代数Ax_tau X。这两种结构在本方法中是统一的。所得结果在数学物理中是适用的。交叉积代数Ax_tau X的乘子代数包含Weyl算子{W（x），x in X}.它们满足正则对易关系。C* 乘法器量子时空作为一个例子进行了讨论。
英文摘要：
The notion of a multiplier of a group X is generalized to that of a C*-multiplier by allowing it to have values in an arbitrary C*-algebra A. On the other hand, the notion of the action of X in A is generalized to that of a projective action of X as linear transformations of the space of continuous functions with compact support in X and with values in A. It is shown that there exists a one-to-one correspondence between C*-multipliers and projective actions. C*-multipliers have been used to define twisted group algebras. On the other hand, the projective action tau can be used to construct the crossed product algebra A x_tau X. Both constructions are unified in the present approach. The results are applicable in mathematical physics. The multiplier algebra of the crossed product algebra A x_tau X contains Weyl operators {W(x),x in X}. They satisfy canonical commutation relations w.r.t. the C*-multiplier. Quantum spacetime is discussed as an example.
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