Related papers: Index a Lie Borel Lie Algebra

In the present paper we present a classification of Lie bialgebra structures on Lie algebras of type g[[u]] and g[u], where g is a simple finite dimensional Lie algebra.

In this paper we show an index theorem for gerbes

We compute the rational Borel equivariant cohomology ring of a cohomogeneity-one action of a compact Lie group.

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

We define a general notion of abstract double Lie algebroid. We show (1) that the double Lie algebroid of a double Lie groupoid is a double Lie algebroid in this sense; (2) that the double cotangent constructed from Lie algebroid structures…

The explicit list of all almost factorizable Lie bialgebra structures on real absolutely simple Lie algebras is given.

The article presents the procedure of the index calculation for the elements of the algebra generated by one dimensional singular integral operators with discontinuous oscillating coefficients.

It is known that the category of Lie algebras over a ring admits algebraic exponents. The aim of this paper is to show that the same is true for the category of internal Lie algebras in an additive, cocomplete, symmetric, closed, monoidal…

Analogous to the types A, B, and C cases, we address the computation of the index of seaweed subalgebras in the type-D case. Formulas for the algebra's index can be computed by counting the connected components of its associated meander. We…

We consider the problem of constructing semisimple subalgebras of real (semi-) simple Lie algebras. We develop computational methods that help to deal with this problem. Our methods boil down to solving a set of polynomial equations. In…

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.

We present a simple and efficient algorithm to compute the sum of the algebraic conjugates of a point on an elliptic curve.

We show that a minimal ideal of a finite-dimensional Lie algebra is either simple or abelian.

We illustrate some simple ideas that can be used for obtaining a classification of small-dimensional solvable Lie algebras.Using these we obtain the classification of 3 and 4 dimensional solvable Lie algebras (over fields of any…

In this paper we investigate the problem of which Lie algebras appear as the derived algebra of a Lie algebra. We present new results that further develop this study and address two questions raised in a paper concerned with the…

The ideals of the Lie algebras of unitriangular polynomial derivations are classified. An isomorphism criterion is given for the Lie factor algebras of the Lie algebras of unitriangular polynomial derivations.

After recalling the notion of Lie algebroid, we construct these structures associated with contact forms or systems. We are then interested in particular classes of Lie Rinehart algebras.

This is an overview article on Lie algebroids, and their role as the infinitesimal counterparts of Lie groupoids.

We introduce anyonic Lie algebras in terms of structure constants. We provide the simplest examples and formulate some open problems.

We give an algorithm for constructing the algebraic hull of a given matrix Lie algebra in characteristic zero. It is based on an algorithm for finding integral linear dependencies of the roots of a polynomial, that is probably of…