# 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.

#### 27 Citations

The quantum two-dimensional Poincaré group from quantum group contraction

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A new derivation of the algebra of functions on the two‐dimensional Euclidean Poincare group is proposed. It is based on a contraction of the Hopf algebra Fun(SOq(3)), where the deformation parameter… Expand

An R-matrix approach to the quantization of the Euclidean group E(2)

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The R-matrices for two different deformations of the Euclidean group E(2), calculated in a two-dimensional representation, are used to determine the deformed Hopf algebra of the representative… Expand

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Abstract Using differential and integral calculi on the quantum plane which are invariant with respect to quantum inhomogeneous Euclidean group E(2) q , we construct the path integral representation… Expand

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We propose a contraction of the de sitter quantum group leading to a Poincare quantum group in any dimensions. The method relies on the coaction of the de Sitter quantum group on a non-commutative… Expand

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The left regular representation of the quantum algebras slq(2) and eq(2) are discussed and shown to be related by contraction. The reducibility is studied andq-difference intertwining operators are… Expand

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Inhomogeneous quantum groups obtained by contraction of semisimple ones are shown to be a natural symmetry for dynamical systems on a lattice. The pseudoeuclidean group in dimensions 1 + 1 is applied… Expand

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The concept of a universal T matrix, introduced by Fronsdal and Galindo (1993) in the framework of quantum groups, is discussed here as a generalization of the exponential mapping. New examples… Expand

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