Abstract The equivariant method of moving frames is applied to formulate a systematic method for explicitly determining general equivariant maps and thereby establishing a nonlinear generalization of a formula attributed to Malgrange.

Abstract We introduce the notion of isoclinism between central extensions in the category of algebras with bracket. We provide several equivalent conditions under which algebras with bracket are isoclinic. We also study the connection between isoclinism and the Schur multiplier of algebras with bracket. It is shown that for finite-dimensional central extensions of algebras with bracket with same dimension, the notion of isoclinism and isomorphism are equivalent. Furthermore, we indicate that all stem covers of an algebra with bracket are isoclinic.

Abstract In this paper, we investigate the differential smoothness of skew PBW extensions over commutative polynomial rings on one and two indeterminates.