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

Eriksen, Eivind

J. Gen. Lie Theory Appl. 5, Article ID G110109, 5 p. (2011).

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

Keywords:

deformation functors; generalized Burnside theorem; noncommutative deformations

Citations:

Zbl 1013.16018