Constants of formal derivatives of non-associative algebras, Taylor expansions and applications (Q996943)

Let \(K\) be a field of characteristic \(0\), \(X\) an ordered set, and denote by \(K\{X\}\) the free unital nonassociative algebra on \(X\). This algebra is endowed with natural derivations \({\partial\;\over\partial x}\) for any \(x\in X\), and so is each quotient \(R=K\{ X\}/I\), for any ideal which is invariant under these derivations. The paper under review is devoted to study some Taylor-like formulas for elements in these algebras, in terms of elements annihilated by the derivations (called \`\` constants\'\') and operations in the multiplication algebra. Methods for the description of the constants by means of the representation theory of the general linear groups or the symmetric groups are presented.