Related papers: Notes sur l'indice des alg\`ebres de Lie (II)
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
In these notes we focus on commutative finite-dimensional normed algebras and some basic examples.
We construct certain Steinberg groups associated to extended affine Lie algebras and their root systems. Then by the integration methods of Kac and Peterson for integrable Lie algebras, we associate a group to every tame extended affine Lie…
A ($2k+1$)$-$dimensional contact Lie algebra is one which admits a one-form $\varphi$ such that $\varphi \wedge (d\varphi)^k\ne0$. Such algebras have index one, but this is not generally a sufficient condition. Here we show that index-one…
L'objet de cet article d'exposition est de pr\'esenter une introduction \`a l'article "The ext algebra of a quantized cycle" \'ecrit en collaboration avec Damien Calaque, et d'expliquer plus g\'en\'eralement comment le dictionnaire entre…
This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results are new. The article can be viewed as a…
Rejoinder: Bayesian Checking of the Second Levels of Hierarchical Models [arXiv:0802.0743]
The complete enriched Lie algebras constitue the natural extension of graded Lie algebras for connected spaces. Each complete enriched Lie algebra is the rational homotopy Lie algebra of a connected space. This text is the first part of a…
We present Hausdorff versions for Lie Integration Theorems 1 and 2 and apply them to study Hausdorff symplectic groupoids arising from Poisson manifolds. To prepare for these results we include a discussion on Lie equivalences and propose…
In this note we answer the two questions raised by Y.Y Li and L. Nguyen in their note [LN2] below.
This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finitely based. (ii) We give examples of important varieties with…
Let g be a complex simple Lie algebra and b a fixed Borel subalgebra of g. We shall describe the abelian ideals of b in a uniform way, that is, independent of the classification of complex simple Lie algebras.
Work in progress concerning alternative formalizations of arithmetic.
We give a presentation of abelian class field theory.
This is a survey paper on Alegbraic Geometry over Lie Algebras
These Lecture Notes are a brief introduction to the Malliavin calculus. In particular, different notions of Malliavin derivative found in the literature are considered and compared.
Expanded lecture notes. Preliminary version, comments are welcome.
This is an expository and introductory note on some results obtained in "Coisotropic embeddings in Poisson manifolds" (ArXiv math/0611480). Some original material is contained in the last two sections, where we consider linear Poisson…
The main aim of this paper is to classify the distinct multiplicative Lie algebra structures (up to isomorphism) on a given group. We also see that for a given group $G$, every homomorphism from the non-abelian exterior square $G \wedge G$…
We consider finite-dimensional complex Lie algebras admitting a periodic derivation, i.e., a nonsingular derivation which has finite multiplicative order. We show that such Lie algebras are at most two-step nilpotent and give several…