The generalized Burnside theorem in noncommutative deformation theory.(English)Zbl 1218.16017

Summary: Let $$A$$ be an associative algebra over a field $$k$$, and let $$\mathcal M$$ be a finite family of right $$A$$-modules. A study of the noncommutative deformation functor $$\text{Def}_{\mathcal M}$$ of the family $$\mathcal M$$ leads to the construction of the algebra $$\mathcal O^A(\mathcal M)$$ of observables and the generalized Burnside theorem, due to O. A. Laudal [Homology Homotopy Appl. 4, No. 2(2), 357-396 (2002; Zbl 1013.16018)]. In this paper, we give an overview of aspects of noncommutative deformations closely connected to the generalized Burnside theorem.

MSC:

 16S80 Deformations of associative rings 16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras 14D15 Formal methods and deformations in algebraic geometry

Zbl 1013.16018
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