Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trees, Amalgams and Calogero-Moser Spaces   We describe the structure of the automorphism groups of algebras Morita
equivalent to the first Weyl algebra $ A_1 $. 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 r\^ole in our approach
is played by a transitive action of the automorphism group of the free algebra
$ \c < x, y > $ on the Calogero-Moser varieties $ \CC_n $ defined in \cite{BW}.
Our results generalize well-known theorems of Dixmier and Makar-Limanov on
automorphisms of $ A_1 $, answering an old question of Stafford (see
\cite{St}). Finally, we propose a natural extension of the Dixmier Conjecture
for $ A_1 $ to the class of Morita equivalent algebras.

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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: quant-ph