有限Hopf C^＊-代数的表示与对偶

Representation and Duality of Finite Hopf C~*-Algebra

设A是有限维Hopf C-代数,H是Hilbert空间.如果存在A在L(H)上的作用γ,在此作用下,L(H)成为具有共轭性质的模代数且H上内积是A-不变的,则A存在惟一的C-表示(θ,H),L(H)的A-不变子空间恰好是θ(A)的换位子.

Suppose that A is a finite dimensional Hopf C-algebra and H is a Hilbert space. If there exists an action γ of A on L(H) so that L(H) is a modular algebra with conjugate property and the inner-product on H is A-invariant, then there is a unique C-representation θ of A on H supplemented by the γ. The A-invariant subspace of L(H) is exactly the commutant of θ(A).