Quantum Affine Transformation Group and Covariant Differential Calculus
Abstract
We discuss quantum deformation of the affine transformation group and its Lie algebra in one-dimensional space. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators. It is also shown that the quantum algebra does not have a universal R-matrix. We present a new method to construct the quantum deformation of the affine transformation group. The method is based on the quantum algebra and the adjoint representation. Furthermore, we construct a differential calculus which is covariant with respect to the action of the quantum affine transformation group.
- Publication:
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Progress of Theoretical Physics
- Pub Date:
- June 1994
- DOI:
- 10.1143/ptp/91.6.1065
- arXiv:
- arXiv:hep-th/9308049
- Bibcode:
- 1994PThPh..91.1065A
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- LaTeX 22 pages OS-GE-34-94 RCNP-058