1996/03/12 by Jan Sobczyk, J Sobczyk
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.QA #q-alg
paper · pdf · doi:10.1088/0305-4470/29/11/022
8 pages, plain TEX, harvmac, to appear in J. Phys. A
arxiv created 1996/03/12 · openalex publication_date 1996/06/07 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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).