Related papers: Notes sur l'indice des alg\`ebres de Lie (II)

Analogue of Springer's formula for the Poincar\'e series of the algebra invariants of ternary form is found.

We study the possibility of factoring a covariant distribution on reductive Lie algebras as finite sum of products of an invariant distribution by a covariant polynomial.

In this paper, we give a complete classification of extensions of finite irreducible conformal modules over rank two Lie conformal algebras.

The goal of this note is to provide a constructive version of the proof of local structure of etale algebras.

In this paper, we introduce the notion of derivations of Lie 2-algebras and construct the associated derivation Lie 3-algebra. We prove that isomorphism classes of non-abelian extensions of Lie 2-algebras are classified by equivalence…

We give a complete description of Lie algebras graded by an infinite irreducible locally finite root system.

These notes include introductory material on the notion of splitting fields for modules over a k-algebra where k is a field.

This is a continuation of arXiv:0903.0398 [math.RT]. Let g be a simple Lie algebra. In this note, we provide simple formulae for the index of sl(2)-subalgebras in the classical Lie algebras and a new formula for the index of the principal…

This is a short survey on the recent developments made in the integration theory with effective formulas of algebraic structures stronger or higher than Lie algebras.

Let g=g_0+ g_1 be a simple Z_2-graded Lie algebra and let b_0 be a fixed Borel subalgebra of g_0. We describe and enumerate the abelian b_0-stable subalgebras of g_1.

In these informal notes, we continue to explore p-adic versions of Heisenberg groups and some of their variants, including the structure of the corresponding Cantor sets.

These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

In this article, we introduce a new cohomology theory associated to a Lie 2-algebras. This cohomology theory is shown to extend the classical cohomology theory of Lie algebras; in particular, we show that the second cohomology group…

In this thesis, we introduce a new cohomology theory associated to a Lie 2-algebras and a new cohomology theory associated to a Lie 2-group. These cohomology theories are shown to extend the classical cohomology theories of Lie algebras and…

A sufficient condition for the simplicity of induced modules of reductive Lie algebras is given.

These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.

Series of short contributions that are part of Nobel Symposium 162 - Microfluidics arXiv:1712.08369.

Analogous to the sl(n) case, we address the computation of the index of seaweed subalgebras of sp(2n) by introducing graphical representations called symplectic meanders. Formulas for the algebra's index may be computed by counting the…

Adjoint functors between the categories of crossed modules of dialgebras and Leibniz algebras are constructed. The well-known relations between the categories of Lie, Leibniz, associative algebras and dialgebras are extended to the…

Expressions for the derivatives of the Legendre polynomials of the first kind with respect to the order of these polynomials are given. An explicit form for the fourth derivative is presented.