探討量子形變的新途徑

Abstract

q-形變在許多數學及物理的不同領域裡被廣泛討論。然而，所有已知的討論都是建立在保角變換 x-> qx 之上。在本篇論文中，我們考慮另一種形式的形變，稱之為 q~-形變，它是建立在 x-> x^q 的變換之上。換言之，這類形變發生在變數 x 的次方數上。我們也期待 q~-形變最終會是研究量子群理論的另一途徑。

The q-deformation had been wide discussed in many different fields of physics and mathematics. However, all the discussions that we know of are simply based on the conformal mapping x-> qx. Throughout the thesis, we consider deformation of another kind, says q~-deformation, which is based on the mapping x-> x^q. In other words, these kinds of deformations appear in the power of variable x. We expect q~- deformation to be a new approach to the studying of Quantum Groups eventually.