Related papers: New Lie tori from Naoi tori
We propose a new simplified definition of extended affine Lie algebras (EALAs for short), and also discuss a general version of extended affine Lie algebras, called locally extended affine Lie algebras (LEALAs for short). We prove a…
Axioms for the generalization of root systems were defined and classified (irreducible) by V. Serganova, which precisely correspond to the root systems of basic classical Lie Superalgebras. Here, we present a unified method for constructing…
Following Sullivan's spacial realization of a differential algebra, we construct a universal integrating Lie 2-groupoid for every Lie algebroid. Then We show that unlike Lie algebras which one-to-one correspond to simply connected Lie…
We introduce the notion of locally finite root supersystems as a generalization of both locally finite root systems and generalized root systems. We classify irreducible locally finite root supersystems.
In this paper we introduce the notion of pure non-characteristically nilpotent Lie algebra and under a condition we prove that a complex maximal extension of a finite-dimensional pure non-characteristically nilpotent Lie algebra is…
On a compact connected Lie group $G$, we study the global solvability and the cohomology spaces of the differential complex associated with an essentially real involutive structure that is invariant under left translations. We prove that…
In this paper we introduce the notion of generalized Lie algebroid and we develop a new formalism necessary to obtain a new solution for the Weistein's Problem. Many applications emphasize the importance and the utility of this new…
Given a fine abelian group grading on a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero, with universal grading group $G$, it is shown that the induced grading by the free group $G/\tor(G)$ is…
We classify the automorphic Lie algebras of equivariant maps from a complex torus to $\mathfrak{sl}_2(\mathbb{C})$. For each case we compute a basis in a normal form. The automorphic Lie algebras correspond precisely to two disjoint…
We investigate a new class of Lie algebras, which are tame locally extended affine Lie algebras of nullity 1. It is an infinite-rank analog of affine Lie algebras, and their centerless cores are a local version of loop algebras. Such…
This article provides a complete characterization of the conformal classes of product tori and standard flat tori in complex dimension 1 (real dimension 2). Utilizing basic differential geometry methods, our approach contrasts with…
In this thesis we describe the universal central extension of two important classes of so-called root-graded Lie algebras defined over a commutative associative unital ring $k.$ Root-graded Lie algebras are Lie algebras which are graded by…
Our aim is to precisely present a tame topology counterpart to canonical stratification of a Lie groupoid. We consider a definable Lie groupoid in semialgebraic, subanalytic, o-minimal over $\mathbb{R}$, or more generally, Shiota's…
The notion of a "root base" together with its geometry plays a crucial role in the theory of finite and affine Lie theory. However, it is known that such a notion does not exist for the recent generalizations of finite and affine root…
A Lie group is a group that is also a differentiable manifold, such that the group operation is continuous respect to the topological structure. To every Lie group we can associate its tangent space in the identity point as a vector space,…
The characterization of systems of differential equations admitting a superposition function allowing us to write the general solution in terms of any fundamental set of particular solutions is discussed. These systems are shown to be…
For a simple Lie algebra $\mathfrak g$ we define a system of linear ODEs with polynomial coefficients, which we call the topological equation of $\mathfrak g$-type. The dimension of the space of solutions regular at infinity is equal to the…
In this note we construct an infinite-dimensional Lie group structure on the group of vertical bisections of a regular Lie groupoid. We then identify the Lie algebra of this group and discuss regularity properties (in the sense of Milnor)…
We introduce Riemannian Lie algebroids as a generalization of Riemannian manifolds and we show that most of the classical tools and results known in Riemannian geometry can be stated in this setting. We give also some new results on the…
In a previous paper, we introduce and study formal manifolds, which generalize smooth manifolds. In this paper, we establish the basic theory of formal Lie groups, which are group objects in the category of formal manifolds. In particular,…