Quantum E(2) groups and Lie bialgebra structures

Details Quantum E(2) groups and Lie bialgebra structures Quantum E(2) groups and Lie bialgebra structures

1996-03-12

arxiv.org/abs/q-alg/9603009v1

Mathematics

Quantum Algebra

8 pages, plain TEX, harvmac, to appear in J. Phys. A

Scientific paper

10.1088/0305-4470/29/11/022

Lie bialgebra structures on $e(2)$ are classified. For two Lie bialgebra structures which are not coboundaries (i.e. which are not determined by a classical $r$-matrix) we solve the cocycle condition, find the Lie-Poisson brackets and obtain quantum group relations. There is one to one correspondence between Lie bialgebra structures on $e(2)$ and possible quantum deformations of $U(e(2))$ and $E(2)$.

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