Abstract
Lie bialgebra structures on e(2) are classified. For two Lie bialgebra structures which are not coboundaries (i.e. those 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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