Galois orders of symmetric differential operators

• Date: 2017
• Main Authors: Futorny, Vyacheslav, Schwarz, João
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2017
• Subjects: Weyl algebra; invariant differential operators; Galois order; filed of fractions; 13N10; 16D30; 16S32; 16S85
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/442
• Journal Title: Algebra and Discrete Mathematics

In this survey we discuss the theory of Galois rings and orders developed in ([20], [22]) by Sergey Ovsienko and the first author. This concept allows to unify the representation theories of Generalized Weyl Algebras ([4]) and of the universal enveloping algebras of Lie algebras. It also had an impa...