A standard example in noncommutative deformation theory (Q2518919)

\textit{O. A. Laudal} developed the concept of a non--commutative deformation theory [Rev. Mat. Iberoam. 19, No. 2, 509--580 (2003; Zbl 1056.14001)]. One of the main ingredients in this theory is the generalized Burnside theorem: Let \(A\) be a finite dimensional \(k\)--algebra, \(k\) an algebraically closed field. Let \(\mathcal{V}=\{V_i\}_{i=1}^r\) be the family of simple \(A\)--modules and \(\mathcal{H}=(H_{ij})\) be the formal non--commutative moduli of \(\mathcal{V}\), then \(A\simeq \mathcal{O}(\mathcal{V})=(H_{ij}\otimes_k\text{Hom}(V_i, V_j))\). In the paper the commutative generalized Massey products are generalized to the non--commutative deformation theory. An example is given illustrating the generalized Burnside theorem.