Quantum affine transformation group and covariant differential calculus
N. Aizawa, H.-T. Sato
TL;DR
This paper explores the quantum deformation of the affine transformation group, revealing its non-cocommutative Hopf algebra structure, realizations, tensor operators, and a covariant differential calculus.
Contribution
It introduces a new quantum deformation of the affine transformation group with explicit algebraic structures and a covariant differential calculus.
Findings
Quantum algebra has a non-cocommutative Hopf algebra structure
Constructed realizations and quantum tensor operators
Developed a covariant differential calculus
Abstract
We discuss quantum deformation of the affine transformation group and its Lie algebra. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators. The deformation of the group is achieved by using the adjoint representation. The elements of quantum matrix form a Hopf algebra. Furthermore, we construct a differential calculus which is covariant with respect to the action of the quantum matrix.
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