Related papers: How Euler would compute the Euler-Poincar\'e chara…
For a restricted Lie superalgebra g over an algebraically closed field of characteristic p > 2, we generalize the deformation method of Premet and Skryabin to obtain results on the p-power and 2-power divisibility of dimensions of…
We consider some parametrized classes of multiple sums first studied by Euler. Identities between meromorphic functions of one or more variables generate reduction formulae for these sums.
We study identities of Lie superalgebras over a field of characteristic zero. We construct a series of examples of finite-dimensional solvable Lie superalgebras with a non-nilpotent commutator subalgebra for which PI-exponent of codimension…
After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.
In this note, we will prove that a finite dimensional Lie algebra $L$ of characteristic zero, admitting an abelian algebra of derivations $D\leq Der(L)$ with the property $$ L^n\subseteq \sum_{d\in D}d(L) $$ for some $n\geq 1$, is…
Results about the following classes of finite-dimensional Lie algebras over a field of characteristic zero are presented: anisotropic (i.e., Lie algebras for which each adjoint operator is semisimple), regular (i.e., Lie algebras in which…
This note studies the behavior of Euler characteristics and of intersection homology Euler characterstics under proper morphisms of algebraic (or analytic) varieties. The methods also yield, for algebraic (or analytic) varieties, formulae…
Following analogous constructions for Lie algebras, we define Whittaker modules and Whittaker categories for finite-dimensional simple Lie superalgebras. Results include a decomposition of Whittaker categories for a Lie superalgebra…
Assume that the coefficients of a polynomial in a complex variable are Laurent polynomials in some complex parameters. The parameter space (a complex torus) splits into strata corresponding to different combinations of coincidence of the…
Various algebraic properties of Heilbronn's exponential sum can be deduced through the use of supercharacter theory, a novel extension of classical character theory due to Diaconis-Isaacs and Andre. This perspective yields a variety of…
In this paper, we study the generalized derivation of a Lie sub-algebra of the Lie algebra of polynomial vector fields on $\mathbb{R}^n$ where $n\geq1$, containing all constant vector fields and the Euler vector field, under some conditions…
"V - E + F = 2", the famous Euler's polyhedral formula, has a natural generalization to convex polytopes in every finite dimension, also known as the Euler-Poincar\'e Formula. We provide another short inductive proof of the general formula.…
In this paper, we extend the concept of Lie superalgebras to a more generalized framework called Super-Lie superalgebras. In addition, they seem to be exploring various supergeneralizations of other algebraic structures, such as…
Lie antialgebras is a class of supercommutative algebras recently appeared in symplectic geometry. We define the notion of enveloping algebra of a Lie antialgebra and study its properties. We show that every Lie antialgebra is canonically…
Master character of the multidimensional homogeneous Euler equation is discussed. It is shown that under restrictions to the lower dimensions certain subclasses of its solutions provide us with the solutions of various hydrodynamic type…
A well-known and old result of Hazewinkel and Koszul states that the cohomology of a finite-dimensional Lie algebra is isomorphic, up to a suitable shift, to its twisted homology, a Lie-theoretical version of Poincare duality. This paper…
An unusual formula for the Euler characteristics of even dimensional triangulated manifolds is deduced from the generalized Dehn-Sommerville equations.
After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras.…
In this note we will present how Euler's investigations on various different subjects lead to certain properties of the Legendre polynomials. More precisely, we will show that the generating function and the difference equation for the…
From the theory of finite dimensional Lie algebras it is known that every finite dimensional Lie algebra is decomposed into a semidirect sum of semisimple subalgebra and solvable radical. Moreover, due to work of Mal'cev the study of…