Locally nilpotent derivations and automorphism groups of certain Danielewski surfaces

We describe the set of all locally nilpotent derivations of the quotient ring K[X,Y, Z]/(f (X)Y - phi(X, Z)) constructed from the defining equation f (X)Y = phi(X, Z) of a generalized Danielewski surface in K-3 for a specific choice of polynomials f and phi, with K an algebraically closed field of characteristic zero. As a consequence of this description we calculate the ML-invariant and the Derksen invariant of this ring. We also determine a set of generators for the group of K-automorphisms of K[X, Y, Z]/(f (X)Y- phi(Z)) also for a specific choice of polynomials f and phi. (C) 2016 Elsevier Inc. All rights reserved.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)UNIFESP, Inst Sci & Technol, Sao Jose Dos Campos, SP, BrazilUFSJ, Dept Math & Phys, Ouro Branco, MG, BrazilUniversidade Federal de São Paulo (UNIFESP), Institute of Science and Technology, São José dos Campos, SP, BrazilCNPq: 462315/2014-2FAPESP: 14/09310-5Web of Scienc