Related papers: The fixed set of the inverse involution on a Lie g…
Hom-Lie superalgebras can be considered as the deformation of Lie superalgebras; which are $\mathbb{Z}_2$-graded generalization of Hom-Lie algebras. The motivation of this paper is to introduce the concept of isoclinism and factor set in…
We determine when there exists a nonzero homomorphism between principal series representations of a complex semisimple Lie group. We also determines the existence of homomorphisms between twisted Verma modules.
Lie symmetry group method is applied to study the Born-Infeld equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra…
A result from Gromov ensures the existence of a contact structure on any connected non-compact odd dimensional Lie group. But in general such structures are not invariant under left translations of the Lie group. The problem of finding…
In this paper, we determine the isomorphism classes of the central simple Poisson algebras introduced earlier by the second author. The Lie algebra structures of these Poisson algebras are in general not finitely-graded.
We classify anti-involutions of Lie superalgebra $\hsd$ preserving the principal gradation, where $\hsd$ is the central extension of the Lie superalgebra of differential operators on the super circle $S^{1|1}$. We clarify the relations…
In this paper, we establish a complete structural description of flat Lorentzian Lie groups, i.e., Lie groups endowed with a flat left invariant Lorentzian metric, thereby resolving a long-standing open problem in the theory of…
We explore when generator-conjugate homomorphisms are conjugate and when element-conjugate homomorphisms are conjugate from abelian or dihedral groups to the symmetric group. We completely determine when such homomorphisms are conjugate in…
Given an algebraic Lie algebra $\mathfrak{g}$ over $\mathbb{C}$, we canonically associate to it a Lie algebra $\mathfrak{g}_{\infty}$ defined over $\mathbb{C}_{\infty}$-the reduction of $\mathbb{C}$ mod infinitely large prime, and show that…
Using an extension to isometries of the associated Sasaki structure, we establish a Lie transformation group structure for the set of isometries of a pseudo-Finsler conical metric.
In this article I describe my recent geometric localization argument dealing with actions of NONcompact groups which provides a geometric bridge between two entirely different character formulas for reductive Lie groups and answers the…
The goal of this paper is to provide a method, based on the theory of extensions of left-symmetric algebras, for classifying left-invariant affine structures on a given solvable Lie group of low dimension. To better illustrate our method,…
This paper deals with affine connections on real manifolds. We give a new characterization of flat affine connections on real manifolds by means of certain affine representations of the Lie group of automorphisms preserving the connection.…
We exploit various inclusions of algebraic groups to give a new construction of groups of type E8, determine the Killing forms of the resulting E8's, and define an invariant of central simple algebras of degree 16 with orthogonal involution…
It is known that that the centralizer of a matrix over a finite field depends, up to conjugacy, only on the type of the matrix, in the sense defined by J. A. Green. In this paper an analogue of the type invariant is defined that in general…
We study left-invariant locally conformally K\"ahler structures on Lie groups, or equivalently, on Lie algebras. We give some properties of these structures in general, and then we consider the special cases when its complex structure is…
For a prime p and natural number n with p greater than or equal to n, we establish the existence of a non-functorial one-to-one correspondence between isomorphism classes of groups of order p^n whose derived subgroup has exponent dividing…
We determine subnormalisers of semisimple elements of prime power order in finite quasi-simple groups of Lie type. For this, we determine the maximal overgroups of normalisers of Sylow tori. This is motivated by the recent character…
We describe the reduction procedure for a symplectic Lie algebroid by a Lie subalgebroid and a symmetry Lie group. Moreover, given an invariant Hamiltonian function we obtain the corresponding reduced Hamiltonian dynamics. Several examples…
Meta-centralizers of non-locally compact group algebras are studied. Theorems about their representations with the help of families of generalized measures are proved. Isomorphisms of group algebras are investigated in relation with…