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

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…

In this paper we study to alternative rings the almost additivity of the Lie multiplicative and Lie triple derivable maps.

We obtain some new inequalities of Chebyshev Type.

This is a survey on extended affine Lie algebras and related types of Lie algebras, which generalize affine Lie algebras.

In 2000, Dergachev and Kirillov introduced subalgebras of "seaweed type" in $\mathfrak{gl}(n)$ and computed their index using certain graphs. In this article, those graphs are called type-A meander graphs. Then the subalgebras of seaweed…

The aim of this short survey is to trace back the ingredients going into the derived equivalence classification of Brauer graph algebras and into the proof of the fact that these algebras are closed under derived equivalence.

Discrete analogs of the Lebedev transforms with the product of the modified Bessel functions are introduced and investigated. Several expansions of suitable functions and sequences in terms of the series and integrals, involving the…

Notes on Commutative Alegbra and Algebraic Geometry covering rings, ideals, modules, presheaves, sheaves, schemes, homological algebra, \'etale cohomology and further topics that are more advanced.

It is shown that any Lie affgebra, that is an algebraic system consisting of an affine space together with a bi-affine bracket satisfying affine versions of the antisymmetry and Jacobi identity, is isomorphic to a Lie algebra together with…

In this paper we give a proof of an index theorem by Bismut. As a consequence we obtain another proof of the Grothendieck-Riemann-Roch theorem in differential cohomology.

The aim of this short note is to give counterexamples to two results by D. Y. Gao [5, Th. 16], [4, Th. 2] and to improve a related result by S.-C. Fang, D. Y. Gao, R.-L. Sheu and S.-Y. Wu [1, Th. 3].

We show that induced representations for a pair of $\textit{diffeological Lie groups}$ exist, in the form of an indexed colimit in the category of diffeological spaces.

We show how the Lie group analysis method can be used in order to obtain first integrals of any system of ordinary differential equations. The method of reduction/increase of order developed by Nucci (J. Math. Phys. 37, 1772-1775 (1996)) is…

In the paper are proved theorems, which amplify the results of my paper "On the difference equation of Poincare type (Part 3)", Max-Plank-Institut fuer Mathematik, Bonn, Preprint Series, 2004, 09, 1-34.

The note complements topological aspects of the theory of chiral algebras.

We establish combinatorial formulas for the index of a class of matrix Lie algebras whose matrix forms are encoded by strict partial orderings.

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…

In this short note, we study the rank of a restricted Lie algebra $(\mathfrak{g},[p])$ and give some applications, which concerns the dimensions of non-trivial irreducible modules. We also compute the rank of the restricted contact algebra…

We compute the arc index of an adequate link and establish bounds on the arc index of the closure of a positive 3-braid. We also conjecture an inequality between the crossing number, arc index, and Turaev genus of a link and show the…

We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.