Spectral Decomposition and Baxterization of Exotic Bialgebras and Associated Noncommutative Geometries

Abstract

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 R03 and R14 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, respectively, three, projectors. These projectors are then used to provide the baxterization procedure with one, respectively, 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 nonstandard features which are noted. Such features show the importance of systematic study of all bialgebras of four generators.