Duality for Exotic Bialgebras

Details Duality for Exotic Bialgebras Duality for Exotic Bialgebras

2001-01-19

arxiv.org/abs/math/0101160v1

J.Phys.A34:4065-4082,2001

Mathematics

Quantum Algebra

25 pages, LaTeX2e, using packages: cite, amsfonts, amsmath, subeqn

Scientific paper

10.1088/0305-4470/34/19/308

In the classification of Hietarinta, three triangular $4\times 4$ $R$-matrices lead, via the FRT formalism, to matrix bialgebras which are not deformations of the trivial one. In this paper, we find the bialgebras which are in duality with these three exotic matrix bialgebras. We note that the $L-T$ duality of FRT is not sufficient for the construction of the bialgebras in duality. We find also the quantum planes corresponding to these bialgebras both by the Wess-Zumino R-matrix method and by Manin's method.

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