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Quantum E(2) groups and Lie bialgebra structures

Jan Sobczyk
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Abstract

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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Jan Sobczyk. 1996-03-12. Quantum E(2) groups and Lie bialgebra structures. https://doi.org/10.1088/0305-4470%2F29%2F11%2F022

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