Duality for exotic bialgebras

Citation
D. Arnaudon et al., Duality for exotic bialgebras, J PHYS A, 34(19), 2001, pp. 4065-4082
Citations number
56
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN journal
03054470 → ACNP
Volume
34
Issue
19
Year of publication
2001
Pages
4065 - 4082
Database
ISI
SICI code
0305-4470(20010518)34:19<4065:DFEB>2.0.ZU;2-Z
Abstract
In the classification of Hietarinta, three triangular 4 x 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 dualit y with these three exotic matrix bialgebras, We note that the L-T duality o f FRT is not sufficient for the construction of the bialgebras in duality. We find also the quantum planes corresponding to these bialgebras both by t he Wess-Zumino R-matrix method and by Manin's method.