On trigonometric Calogero-Moser spaces
Zafar NormatovV.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, University street, 9, Olmazor district, Tashkent, 100174, UzbekistanYingqi WangSchool of Mathematics, Jilin University, Changchun, 130012, ChinaShuai ZengSchool of Mathematics, Jilin University, Changchun, 130012, China
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In this paper, we investigate the trigonometric Calogero-Moser space C 3 tri as an irreducible affine variety and analyze the detailed structure of its coordinate ring C [ C 3 tri ] . We establish and optimize the Poisson structure on C 3 tri , deriving the Poisson bracket multiplication table for the generators a 1 , … , a 9 . Furthermore, we identify five defining relations r 1 , … , r 5 among the generators and establish the isomorphism C [ C 3 tri ] ≅ C [ a 1 , … , a 9 ] / I , where I is the ideal generated by the five relations.
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