Jafari, Mohammad Hossein Madadi, Ali Reza
Published in
Forum Mathematicum

In the present paper, right 2-Engel elements, central automorphisms and commuting automorphisms of Lie algebras will be studied. For this purpose, first the structure of the set of all right 2-Engel elements of a Lie algebra will be examined and then, by taking advantage of it, a number of interesting results about central and commuting automorphis...

Chuah, Meng-Kiat Zhang, Mingjing
Published in
Forum Mathematicum

Let 𝔤 ${{\mathfrak{g}}}$ be a simple Lie algebra. Let Aut ( 𝔤 ) ${{\rm Aut}(\mathfrak{g})}$ be the group of all automorphisms on 𝔤 ${\mathfrak{g}}$ , and let Int ( 𝔤 ) ${{\rm Int}(\mathfrak{g})}$ be its identity component. The outer automorphism group of 𝔤 ${\mathfrak{g}}$ is defined as Aut ( 𝔤 ) / Int ( 𝔤 ) ${{\rm Aut}(\mathfrak{g})/{\rm I...

Gavarini, Fabio
Published in
Forum Mathematicum

In this note I fix a mistake in my previous paper [5]: namely, the result concerning the uniqueness (up to isomorphisms) of such supergroups needs a new formulation and proof. By the same occasion, I explain more in detail the existence result which comes out of the construction of Chevalley supergroups.

Gavarini, Fabio
Published in
Forum Mathematicum

I present a construction of connected affine algebraic supergroups 𝐆V associated with simple Lie superalgebras 𝔤 of Cartan type and with 𝔤-modules V. Conversely, I prove that every connected affine algebraic supergroup whose tangent Lie superalgebra is of Cartan type is necessarily isomorphic to one of the supergroups 𝐆V that I introduced. In parti...

Luo, Cuiling Xu, Xiaoping
Published in
Journal of Algebra

In this paper, we study two-parameter Z-graded oscillator representations of symplectic Lie algebras obtained from the natural oscillator representation by partially swapping differential operators and multiplication operators. We prove that the homogeneous subspaces with nonzero degree or unequal parameters are infinite-dimensional irreducible wei...

Wang, Dengyin
Published in
Journal of Algebra

Bai, Wei Liu, Wende Melikyan, Hayk
Published in
Journal of Algebra

Ahmadi, S. Ruhallah Izadi, Mohammad A. Szechtman, Fernando
Published in
Linear Algebra and Its Applications

Wang, Dengyin
Published in
Journal of Algebra

Let g be a simple Lie algebra of rank l over an algebraically closed field of characteristic zero, b a Borel subalgebra of g. An invertible linear map φ on b is said preserving zero Lie products in both directions if for x,y∈b, [x,y]=0 if and only if [φ(x),φ(y)]=0. In this paper, it is shown that an invertible linear map φ on b preserving zero Lie ...

Luo, Cuiling Xu, Xiaoping
Published in
Journal of Algebra