Dixmier群和Calogero-Moser空间的子群

Q3 Mathematics

Electronic Research Announcements in Mathematical Sciences Pub Date : 2011-03-01 DOI:10.3934/ERA.2011.18.12

Y. Berest, A. Eshmatov, F. Eshmatov

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引用次数: 2

摘要

我们描述了与第一Weyl代数等价的代数Morita自同构群的结构。特别地，我们利用群作用于图的Bass-Serre理论，用合并积的形式给出了这些群的几何表示。自由代数$ k $的自同构群对在[5]中定义的Calogero-Moser变元$ \CC_n $的传递作用在我们的方法中发挥了关键作用。最后，我们提出了$ A_1(k) $的Dixmier猜想到Morita等价代数类的一个自然推广。

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On subgroups of the Dixmier group and Calogero-Moser spaces

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 role in our approach is played by a transitive action of the automorphism group of the free algebra $ k $ 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.

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来源期刊

Electronic Research Announcements in Mathematical Sciences 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication. ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007