Related papers: Linear Representation of Lie Group
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
We establish foundational properties of fractional operators on Lie groups of homogeneous type. We prove embedding theorems for the associated Sobolev-type spaces.
Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is…
We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and…
Due to the occurrence of large exceptional Lie groups in supergravity, calculations involving explicit Lie algebra and Lie group element manipulations easily become very complicated and hence also error-prone if done by hand. Research on…
This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.
We study realizations of Lie algebras by vector fields. A correspondence between classification of transitive local realizations and classification of subalgebras is generalized to the case of regular local realizations. A reasonable…
The purpose of the present paper is to study representations and cohomologies of differential 3-Lie algebras with any weight. We introduce the representation of a differential 3-Lie algebra. Moreover,we develop cohomology theory of a…
We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These sixteen Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical…
We introduce the notion of Lusternik-Schnirelmann category for differentiable stacks and establish its relation with the groupoid Lusternik-Schnirelmann category for Lie groupoids.
A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference scheme invariant. The method is applied to…
In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we…
In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation…
In this work we deal with coverings and actions of Lie group- groupoids being a sort of the structured Lie groupoids. Firstly, we define an action of a Lie group-groupoid on some Lie group and the smooth coverings of Lie group-groupoids.…
We study realizations of polynomial deformations of the sl(2,R)- Lie algebra in terms of differential operators strongly related to bosonic operators. We also distinguish their finite- and infinite-dimensional representations. The linear,…
The author has previously shown that solvable Lie A-algebras and complemented solvable Lie algebras decompose as a vector space direct sum of abelian subalgebras, and their ideals relate nicely to this decomposition. However, neither of…
A diverse collection of fusion categories may be realized by the representation theory of quantum groups. There is substantial literature where one will find detailed constructions of quantum groups, and proofs of the…
I review some of my recent work on non-lorentzian geometry. I review the classification of kinematical Lie algebras and their associated Klein geometries. I then describe the Cartan geometries modelled on them and their characterisation in…
Derivations extend the concept of differentiation from functions to algebraic structures as linear operators satisfying the Leibniz rule. In Lie algebras, derivations form a Lie algebra via the commutator bracket of linear endomorphisms.…
Cohen and Taylor introduced Plesken Lie algebras of finite groups and studied their structural properties. As a further step, we will introduce Plesken Lie algebra representations, Plesken Lie algebra modules and discuss the irreducibility…