Cohomology of monoid algebras (Q1320252)

For a commutative \(k\)-algebra \(A\), let \(\text{Def}_ A (-)\) denote the deformation functor. Under some conditions there is a surjection \(\text{Mor} (H,-) \to \text{Def}_ A (-)\) [\textit{M. Schlessinger}, Trans. Am. Math. Soc. 130, 208-222 (1968; Zbl 0167.495)] where the \(k\)-algebra \(H\) is the ``hull'' of the deformation functor. Following the result by \textit{O. A. Laudal} [``Formal moduli of algebraic structures'', Lect. Notes Math. 754 (1979; Zbl 0438.14007)] the author develops a theory for calculating the algebra cohomology of monoid algebras to reduce the problem of finding the hull of the deformation functor to a combinatorial one.