Mathematics – Quantum Algebra
Scientific paper
2002-09-24
Int. J. Mod. Phys. A18 (2003) 4201
Mathematics
Quantum Algebra
14 pages, LaTeX2e, using packages: cite, amsfonts, amsmath, subeqn; v2: small improvements, coincides with journal version
Scientific paper
10.1142/S0217751X03016100
We study the geometric aspects of two exotic bialgebras S03 and S14 introduced in math.QA/0206053. These bialgebras are obtained by the Faddeev-Reshetikhin-Takhtajan RTT prescription with non-triangular R-matrices which are denoted $R_{03}$ and $R_{14}$ in the classification of Hietarinta, and they are not deformations of either GL(2) or GL(1/1). We give the spectral decomposition which involves two, resp., three, projectors. These projectors are then used to provide the Baxterisation procedure with one, resp., two, parameters. Further, the projectors are used to construct the noncommutative planes together with the corresponding differentials following the Wess-Zumino prescription. In all these constructions there appear non-standard features which are noted. Such features show the importance of systematic study of all bialgebras of four generators.
Arnaudon Daniel
Chakrabarti Alok
Dobrev V. K.
Mihov S. G.
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