Spectral Decomposition and Baxterisation of Exotic Bialgebras and Associated Noncommutative Geometries - Archive ouverte HAL
Article Dans Une Revue International Journal of Modern Physics A Année : 2003

Spectral Decomposition and Baxterisation of Exotic Bialgebras and Associated Noncommutative Geometries

Résumé

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.

Dates et versions

hal-00003534 , version 1 (10-12-2004)

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Daniel Arnaudon, Amitabha Chakrabarti, Vladimir Dobrev, Stephan Mihov. Spectral Decomposition and Baxterisation of Exotic Bialgebras and Associated Noncommutative Geometries. International Journal of Modern Physics A, 2003, A18, pp.4201. ⟨hal-00003534⟩
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