BRAIDED GROUPS AND QUANTUM FOURIER-TRANSFORM

[摘要] We show that acting on every finite-dimensional factorizable ribbon Hopf algebra H there are invertible operators Y, T obeying the modular identities (Y T)3 = lambdaL2, where lambda is a constant. The class includes the finite-dimensional quantum groups u(q)(g) associated to complex simple Lie algebras. We give the example of u(q)(sl(2)) at a root of unity in detail, as well as an example relating to anyons. The operator Y plays the role of ''quantum Fourier Transform'' and acts naturally on H viewed by transmutation as a braided group H (a braided-cocommutative Hopf algebra in a braided category). It obeys Y2 = s-1, where s is the antipode of H. The results follow as an application of previous category-theoretical constructions. (C) 1994 Academic Press, Inc.

[发布日期] 1994-06-15