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On subgroups of the Dixmier group and Calogero-Moser spaces

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  • We describe the structure of the automorphism groups of algebras Morita equivalent to the first Weyl algebra $ A_1(k) $. In particular, we give a geometric presentation for these groups in terms of amalgamated products, using the Bass-Serre theory of groups acting on graphs. A key rôle in our approach is played by a transitive action of the automorphism group of the free algebra $ k< x, y>$ on the Calogero-Moser varieties $ \CC_n $ defined in [5]. In the end, we propose a natural extension of the Dixmier Conjecture for $ A_1(k) $ to the class of Morita equivalent algebras.
    Mathematics Subject Classification: Primary: 16S32; Secondary: 14H70, 16W20, 20E08.


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