相关论文: Separation of variables and Lie algebra contractio…
In this paper, first using the higher derived brackets, we give the controlling algebra of relative difference Lie algebras, which are also called crossed homomorphisms or differential Lie algebras of weight 1 when the action is the adjoint…
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…
Contractions of Lie algebras are combined with the classical matrix method of Gel'fand to obtain matrix formulae for the Casimir operators of inhomogeneous Lie algebras. The method is presented for the inhomogeneous pseudo-unitary Lie…
We prove some isomorphisms between exceptional W-algebras associated with exceptional simple Lie algebras.
In this paper, at first the construction of Lie higher derivations and higher derivations on a generalized matrix algebra were characterized; then the conditions under which a Lie higher derivation on generalized matrix algebras is proper…
A description of a ring of functions on the base of a universal formal deformation for several moduli problems is given. The answer is given in terms of a homology group of a certain dg Lie algebra canonically (up to an essentially unique…
We give an explicit description of the Lie algebra of derivations for a class of infinite dimensional algebras which are given by \'etale descent. The algebras under consideration are twisted forms of central algebras over rings, and…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
Let $L$ be a solvable Lie algebra of dimension less than or equal to 4 over finite fields. We compute and record, in explicit symbolic form, the zeta functions enumerating subalgebras or ideals of $L$, and study their properties. We also…
We study Cartan-Subalgebras of Lie-Algebras associated to associative algebras.
A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements require the use of projectors,…
We develop structure theory of finite Lie conformal superalgebras.
For compact sets $K\subset \mathbb C^{d}$, we introduce a subalgebra $A_{D}(K)$ of $A(K)$, which allows us to obtain Mergelyan type theorems for products of planar compact sets as well as for graphs of functions.
The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector…
The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…
We study invariance properties of Colombeau generalized functions under actions of smooth Lie transformation groups. Several characterization results analogous to the smooth setting are derived and applications to generalized rotational…
In this paper we study some fundamental algebraic properties of slice functions and slice regular functions over an alternative $^*$-algebra $A$ over $\mathbb{R}$. These recently introduced function theories generalize to higher dimensions…
The present work is devoted to the extension of some general properties of automorphisms and derivations which are known for Lie algebras to finite dimensional complex Leibniz algebras. The analogues of the Jordan-Chevalley decomposition…
Several new invariants for Lie algebroids have been discovered recently. We give an overview of these invariants and establish several relationships between them.
In this thesis new objects to the existing set of invariants of Lie algebras are added. These invariant characteristics are capable of describing the nilpotent parametric continuum of Lie algebras. The properties of these invariants, in…