Sylvain Lavau
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View article: Supersymmetric Poisson and Poisson-supersymmetric sigma models
Supersymmetric Poisson and Poisson-supersymmetric sigma models Open
A bstract We revisit and construct new examples of supersymmetric 2D topological sigma models whose target space is a Poisson supermanifold. Inspired by the AKSZ construction of topological field theories, we follow a graded-geometric appr…
View article: Atiyah classes of Lie algebroid homotopy modules
Atiyah classes of Lie algebroid homotopy modules Open
For a Lie algebroid pair $A\hookrightarrow L$ we study cocycles constructed from the extension to $L$ of the higher connection forms of a representation up to homotopy $E$ of the Lie algebroid $A$. We show that there exists a cohomology cl…
View article: Evolutionary Psychology and the Naturalization of Gender Inequality
Evolutionary Psychology and the Naturalization of Gender Inequality Open
This article explores the uses of evolutionary psychology in a corpus of 29 articles published by the online magazine Quillette. We show that while they openly rely on a rationalist, descriptive stance, Quillette contributors actively prom…
View article: The modular class of a singular foliation
The modular class of a singular foliation Open
The modular class of a regular foliation is a cohomological obstruction to the existence of a volume form transverse to the leaves which is invariant under the flow of the vector fields of the foliation. By drawing on the relationship betw…
View article: What Is a Theorem (in Practice)? The Role of Metamathematics in the Making of Mathematics
What Is a Theorem (in Practice)? The Role of Metamathematics in the Making of Mathematics Open
This article advocates the benefits of a sociological perspective for the philosophy of mathematical practice. Drawing from the literature of the sociology of sciences, it defends a community-centered approach of the study of mathematical …
View article: From Lie algebra crossed modules to tensor hierarchies
From Lie algebra crossed modules to tensor hierarchies Open
The present paper, though inspired by the use of tensor hierarchies in theoretical physics, establishes their mathematical credentials, especially as genetically related to Lie algebra crossed modules. Gauging procedures in supergravity re…
View article: From differential crossed modules to tensor hierarchies
From differential crossed modules to tensor hierarchies Open
Leibniz algebras have been increasingly used in gauging procedures in supergravity, as it can be shown that embedding tensors naturally induce such algebraic structures. Recent mathematical interpretations of these gauging procedures invol…
View article: $L_\infty$-algebra extensions of Leibniz algebras
$L_\infty$-algebra extensions of Leibniz algebras Open
Leibniz algebras have been increasingly used in gauging procedures in supergravity. Their relationship with $L_\infty$-algebras and tensor hierarchies have been explored in the physics literature. This paper is devoted to showing that a Le…
View article: The Universal Lie $\infty$-Algebroid of a Singular Foliation
The Universal Lie $\infty$-Algebroid of a Singular Foliation Open
We consider singular foliations \mathcal{F} as locally finitely generated \mathscr{O} -submodules of \mathscr{O} -derivations closed under the Lie bracket, where \mathscr{O} is the ring of smooth, holomorphic, or real analytic functions on…
View article: The Universal Lie $\infty$-Algebroid of a Singular Foliation
The Universal Lie $\infty$-Algebroid of a Singular Foliation Open
We consider singular foliations ${\cal F}$ as locally finitely generated $ {\mathscr O}$-submodules of $ {\mathscr O}$-derivations closed under the Lie bracket, where ${\mathscr O}$ is the ring of smooth, holomorphic, or real analytic func…
View article: A short guide through who said what and what is true about singular foliations
A short guide through who said what and what is true about singular foliations Open
The generalization of Frobenius' theorem to foliations with singularities is usually attributed to Stefan and Sussmann, for their simultaneous discovery around 1973. However, their result is often referred to without caring much on the pre…
View article: A systematic approach to tensor hierarchies
A systematic approach to tensor hierarchies Open
Tensor hierarchies are algebraic objects that emerge in gauging procedures in supergravity models, and that present a very deep and intricate relationship with Leibniz (or Loday) algebras. In this paper, we show that one can canonically as…
View article: Tensor hierarchies and Lie $n$-extensions of Leibniz algebras
Tensor hierarchies and Lie $n$-extensions of Leibniz algebras Open
Tensor hierarchies are algebraic objects that emerge in gauging procedures in supergravity models, and that present a very deep and intricate relationship with Leibniz (or Loday) algebras. In this paper, we show that one can canonically as…
View article: Lie $\infty$-algebroids and singular foliations
Lie $\infty$-algebroids and singular foliations Open
A singular (or Hermann) foliation on a smooth manifold $M$ can be seen as a subsheaf of the sheaf $\mathfrak{X}$ of vector fields on $M$. We show that if this singular foliation admits a resolution (in the sense of sheaves) consisting of s…