The two-dimensional quantum Euclidean algebra

@article{Schupp1992TheTQ,
  title={The two-dimensional quantum Euclidean algebra},
  author={Peter Schupp and Paul Watts and Bruno Zumino},
  journal={Letters in Mathematical Physics},
  year={1992},
  volume={24},
  pages={141-145}
}
The algebra dual to Woronowicz's deformation of the two-dimensional Euclidean group is constructed. The same algebra is obtained from SUq(2) via contraction on both the group and algebra levels. 
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References

SHOWING 1-7 OF 7 REFERENCES
Three-dimensional quantum groups from contractions of SU(2) q
Contractions of Lie algebras and of their representations are generalized to define new quantum groups. An explicit and complete exposition is made for the one‐dimensional Heisenberg H(1)q and theExpand
Quantum E(2) group and its Pontryagin dual
The quantum deformation of the group of motions of the plane and its Pontryagin dual are described in detail. It is shown that the Pontryagin dual is a quantum deformation of the group ofExpand
An analogue of P.B.W. theorem and the universalR-matrix forUhsl(N+1)
One uses Drinfeld's quantum double construction and a basis á la Poincaré-Birkhoff-Witt inUhn+ to compute an explicit formula for the quantumR-matrix.
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)Expand
Notes in Phys
  • Proc. X-th IAMP Conf
  • 1991
J. Math. Phys
  • J. Math. Phys
  • 1990
Commun. Math. Phys
  • Commun. Math. Phys
  • 1989