Invariante de Makar-Limanov de certas hipersuperfícies algébricas

Abstract

The Makar-Limanov invariant ML(B) of an a-ne k-algebra B (with k a -eld, which will be typically assumed to be of characteristic zero) is a very important invariant, defined in terms of the kernels of suitable derivations of B called locally nilpotent derivations. The theme has connections to various central problems in Commutative Algebra, for instance, the Jacobian Conjecture, the Fourteenth Hilbert's Problem, and the Cancellation Problem, and has been investigated by many authors. In this work, after the presentation of basic concepts and results, our main goal is the explicit obtainment of the structure of ML(B) (as a k-algebra) when B is the coordinate ring of certain special a-ne algebraic hypersurfaces, to wit, the so-called Danielewski surfaces, as well as the famous Makar-Limanov 3-fold defined by x + x2y + z2 + t3 = 0.