Inhomogeneous Quantum Groups IGLq,r(N):. Universal Enveloping Algebra and Differential Calculus
Abstract
A review of the multiparametric linear quantum group GLq,r(N), its real forms, its dual algebra U[glq,r(N)] and its bicovariant differential calculus is given in the first part of the paper. We then construct the (multiparametric) linear inhomogeneous quantum group IGLq,r(N) as a projection from GLq,r(N+1) or, equivalently, as a quotient of GLq,r(N+1) with respect to a suitable Hopf algebra ideal. A bicovariant differential calculus on IGLq,r(N) is explicitly obtained as a projection from that on GLq,r(N+1). Our procedure unifies in a single structure the quantum plane coordinates and the q group matrix elements Tab, and allows one to deduce without effort the differential calculus on the q plane IGLq,r(N)/GLq,r(N). The general theory is illustrated on the example of IGLq,r(2).
- Publication:
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International Journal of Modern Physics A
- Pub Date:
- 1996
- DOI:
- 10.1142/S0217751X96000481
- arXiv:
- arXiv:hep-th/9408031
- Bibcode:
- 1996IJMPA..11.1019A
- Keywords:
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- High Energy Physics - Theory;
- Mathematics - Quantum Algebra
- E-Print:
- 38 pages