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.


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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