On the Theory of Quantum Groups

May 30, 1989
10 pages
Published in:
  • Lett.Math.Phys. 19 (1990) 121
Report number:
  • ORSAY-LPTHE-89-20-REV,
  • ORSAY-LPTHE-89-20

Citations per year

199219941996199820002103
Abstract: (Springer)
By using the results of S. L. Woronowicz, we show that for the twisted version of the classical compact matrix groups, the Hopf algebraAh of representative elements is isomorphic as a co-algebra to the Hopf algebraAO of representative functions on the classical group. As a consequence,Ah can be identified withAO as a co-algebra but with an associative product, called the star-product, which is a deformation of the original commutative product ofAO. Furthermore, the construction of this star product from the original product is connected to the Fourier transformation in a manner which is similar to the construction of quantum mechanics from classical mechanics on phase space. In fact, we shall describe the analog of the Weyl correspondence.
Note:
  • Revised version