Search results for " derivations."

showing 4 items of 4 documents

Rationally integrable vector fields and rational additive group actions

2016

International audience; We characterize rational actions of the additive group on algebraic varieties defined over a field of characteristic zero in terms of a suitable integrability property of their associated velocity vector fields. This extends the classical correspondence between regular actions of the additive group on affine algebraic varieties and the so-called locally nilpotent derivations of their coordinate rings. Our results lead in particular to a complete characterization of regular additive group actions on semi-affine varieties in terms of their associated vector fields. Among other applications, we review properties of the rational counterpart of the Makar-Limanov invariant…

Integrable systemRationally integrable derivationsGeneral Mathematics010102 general mathematics05 social sciencesLocally nilpotentAlgebraic variety01 natural sciencesLocally nilpotent derivations[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]AlgebraHomogeneousRational additive group actions0502 economics and businessVector fieldAffine transformation[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]050207 economics0101 mathematicsInvariant (mathematics)MSC: 14E07 14L30 14M25 14R20Additive groupMathematics
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Derivations of the (n, 2, 1)-nilpotent Lie Algebra

2016

In this paper, we study derivations of the (2, n, 1)-nilpotent Lie Algebra

Statistics and ProbabilityPure mathematicsApplied MathematicsGeneral Mathematics010102 general mathematics010103 numerical & computational mathematics01 natural sciencesAlgebraNilpotent Lie algebraSettore MAT/03 - GeometriaDerivation0101 mathematicsNilpotent Lie Algebras derivations.MathematicsJournal of Mathematical Sciences
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Unbounded derivations and *-automorphisms groups of Banach quasi *-algebras

2018

This paper is devoted to the study of unbounded derivations on Banach quasi *-algebras with a particular emphasis to the case when they are infinitesimal generators of one parameter automorphisms groups. Both of them, derivations and automorphisms are considered in a weak sense; i.e., with the use of a certain families of bounded sesquilinear forms. Conditions for a weak *-derivation to be the generator of a *-automorphisms group are given.

Unbounded derivationPure mathematicsAutomorphisms groups and their infinitesimal generatorsInfinitesimalBanach quasi *-algebra01 natural sciencesMathematics::Group Theory*-Automorphisms groups and their infinitesimal generatorSettore MAT/05 - Analisi Matematica0103 physical sciencesFOS: MathematicsAutomorphisms groups and their infinitesimal generators; Banach quasi; Integrability of derivation; Unbounded derivations; Automorphisms groups and their infinitesimal generators; Banach quasi; Integrability of derivation; Unbounded derivationsBanach quasi0101 mathematicsOperator Algebras (math.OA)MathematicsGroup (mathematics)Applied Mathematics010102 general mathematicsIntegrability of derivationMathematics - Operator AlgebrasAutomorphismUnbounded derivationsFunctional Analysis (math.FA)Mathematics - Functional AnalysisBounded function010307 mathematical physicsGenerator (mathematics)
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Embeddings of Danielewski hypersurfaces

2008

In this thesis, we study a class of hypersurfaces in $\mathbb{C}^3$, called \emph{Danielewski hypersurfaces}. This means hypersurfaces $X_{Q,n}$ defined by an equation of the form $x^ny=Q(x,z)$ with $n\in\mathbb{N}_{\geq1}$ and $\deg_z(Q(x,z))\geq2$. We give their complete classification, up to isomorphism, and up to equivalence via an automorphism of $\mathbb{C}^3$. In order to do that, we introduce the notion of standard form and show that every Danielewski hypersurface is isomorphic (by an algorithmic procedure) to a Danielewski hypersurface in standard form. This terminology is relevant since every isomorphism between two standard forms can be extended to an automorphism of the ambiant …

polynomial automorphisms.Danielewski surfacespolynômes équivalentsequivalent polynomialslocally nilpotent derivations[MATH] Mathematics [math]dérivations localement nilpotentesstable equivalence problemDanielewski hypersurfacessurfaces de Danielewskihypersurfaces de Danielewskiproblème de l'équivalence stableautomorphismes polynomiaux
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