2 citations · 3 across the 10 of their papers we have counts for
11 papers
The symplectic leaves of the affine Poisson -scheme associated with a singular subalgebroid
Ruben Louis
Every singular subalgebroid, and in particular every singular foliation , determines a universal Poisson -scheme , w…
Lie-Rinehart and Poisson algebras over -rings
Eugene Lerman, Ruben Louis
We define the analogue of Lie-Rinehart algebras over -rings. We show that given a Poisson -ring its module of -Käh…
On construction of differential -graded varieties
Aliaksandr Hancharuk, Ruben Louis
Given a commutative unital algebra , a proper ideal in , and a positively graded differential variety over , we provide…
On longitudinal differential operators and Nash blowups
Ruben Louis
In this short note, we describe the Helffer-Nourrigat cone of a singular foliation in terms of the Nash algebroid associated to the foliation. Along the way, we show that the Helff…
The holonomy Lie -groupoid of a singular foliation I
Camille Laurent-Gengoux, Ruben Louis
We construct a finite-dimensional higher Lie groupoid integrating a singular foliation , under the mild assumption that the latter admits a geometric resolution. More…
An invitation to singular foliations
Camille Laurent-Gengoux, Ruben Louis, Leonid Ryvkin
These lecture notes attempt to invite the reader towards the theory of singular foliations, both smooth and holomorphic. In addition to a systematic review of the foundations, and…
On Nash resolution of (singular) Lie algebroids
Ruben Louis
Any Lie algebroid admits a Nash-type blow-up that sits in a nice short exact sequence of Lie algebroids $0\rightarrow K\rightarrow \mathrm{Nash}(A)\rightarro…
Universal higher Lie algebras of singular spaces and their symmetries
Ruben Louis
The results of this manuscript is the collection of my articles that I published during my PhD thesis. We show that there is an equivalence of categories between Lie-Rinehart algeb…
A series of Nash resolutions of a singular foliation
Ruben Louis
We construct a series of blowups of a singular foliation by applying to the universal Lie -algebroid of a singular foliation the s…
On symmetries of singular foliations
Ruben Louis
This paper shows that a weak symmetry action of a Lie algebra on a singular foliation induces a unique up to homotopy Lie-morphism from $\mathfr…
Lie-Rinehart algebra acyclic Lie -algebroid
Camille Laurent-Gengoux, Ruben Louis
We show that there is an equivalence of categories between Lie-Rinehart algebras over a commutative algebra and homotopy equivalence classes of negatively graded Lie…