Related papers: Notes sur l'indice des alg\`ebres de Lie (II)
An improved (streamlined and extended) version of this paper is available as math.RA/0203010, which however omits some details. We recommend the later version unless details are essential.
We give an explicit description of the Lie algebra of derivations for a class of infinite dimensional algebras which are given by \'etale descent. The algebras under consideration are twisted forms of central algebras over rings, and…
The author has previously shown that solvable Lie A-algebras and complemented solvable Lie algebras decompose as a vector space direct sum of abelian subalgebras, and their ideals relate nicely to this decomposition. However, neither of…
This expository note outlines why it is sometimes useful to consider the bigraded type A link homology theories as associated with the Lie algebras gl(N) instead of sl(N).
The aim of this article is to find all weight modules of degree 1 of a simple complex Lie algebra that integrate to a continuous representation of a simply-connected real Lie group on some Hilbert space.
This paper is, essentially, a survey related to the problem of understanding the combinatorics of the action of the monoidal category of finite dimensional modules over a simple finite dimensional Lie algebra on various categories of Lie…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
This note is the follow up to a paper by M. Waldschmidt.
The notions of \emph{Poisson Lie group} and \emph{Poisson homogeneous space} are extended to the Dirac category. The theorem of Drinfel$'$d (\cite{Drinfeld93}) on the one-to-one correspondence between Poisson homogeneous spaces of a Poisson…
This note gives a simple approach to q-analogues of some results associated with Abel polynomials.
This is a brief overview of a few selected chapters on automorphism groups of affine varieties. It includes some open questions.
For a Lie groupoid there is an analytic index morphism which takes values in the $K-$theory of the $C^*$-algebra associated to the groupoid. This is a good invariant but extracting numerical invariants from it, with the existent tools, is…
Supplementary results obtained after the completion of our previous paper are given together with discussing some examples. A quick review of the previous paper is also included.
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
We have already conjectured 2 important guesses regarding Hypo-Lie algebra and modular simple Lie algebra. We would like to attach 2 important guesses more to this conjecture. Such new guesses are related to the Steinberg module.
We introduce Poisson double algebroids, and the equivalent concept of double Lie bialgebroid, which arise as second-order infinitesimal counterparts of Poisson double groupoids. We develop their underlying Lie theory, showing how these…
$n$-ary algebras of the first degeneration level are described. A detailed classification is given in the cases $n=2,3$.
We classify a class of infinite-dimensional simple graded pre-Lie algebras on the graded vector space underlying the algebra of Laurent polynomials, with a specific form for the product.
Categories of W*-bimodules are shown in an explicit and algebraic way to constitute an involutive W*-bicategory.
We classify Lie n-algebras possessing an invariant lorentzian inner product.