Tang, Xiaomin Yang, Yu
Published in
Open Mathematics

The Witt algebra 𝔚d of rank d(≥ 1) is the derivation algebra of Laurent polynomial algebras in d commuting variables. In this paper, all biderivations of 𝔚d without anti-symmetric condition are determined. As an applications, commutative post-Lie algebra structures on 𝔚d are obtained. Our conclusions recover and generalize results in the related pa...

Boukas, Andreas Feinsilver, Philip Fellouris, Anargyros
Published in
Random Operators and Stochastic Equations

We study the structure of zero row sum matrices as an algebra and as a Lie algebra in the context of groups preserving a given projection in the algebra of matrices. We find the structure of the Lie algebra of the group that fixes a given projection. Details for the zero row sum matrices are presented. In particular, we find the Levi decomposition ...

Falcone, Giovanni Figula, Ágota
Published in
Forum Mathematicum

We classify finite-dimensional real nilpotent Lie algebras with 2-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to SO 2 ( ℝ ) ${{\mathrm{SO}}_{2}(\mathbb{R})}$ . This is the first step to extend the class of nilpotent Lie algebras 𝔥 ${{\mathfrak{h}}}$ of type { n , 2 } ${\{n,2\}}$ to solvable Lie algebras...

Goze, Michel Remm, Elisabeth
Published in
Georgian Mathematical Journal

The classification of complex or real finite dimensional Lie algebras which are not semi simple is still in its early stages. For example, the nilpotent Lie algebras are classified only up to dimension 7. Moreover, to recognize a given Lie algebra in the classification list is not so easy. In this work, we propose a different approach to this probl...

Lau, Michael
Published in
Journal of Pure and Applied Algebra

We use evaluation representations to give a complete classification of the finite-dimensional simple modules of twisted current algebras. This generalizes and unifies recent work on multiloop algebras, current algebras, equivariant map algebras, and twisted forms.

Duong, Minh Thanh Ushirobira, Rosane

In this paper, we generalize some results on quadratic Lie algebras to quadratic Lie superalgebras, by applying graded Lie algebras tools. We establish a one-to-one correspondence between non-Abelian quadratic Lie superalgebra structures and nonzero even super-antisymmetric 3-forms satisfying a structure equation. An invariant number of quadratic L...

Lau, Michael
Published in
Journal of Pure and Applied Algebra

BAI, Ruipu CHENG, Yu LIE, Jiaqian MENG, Wei
Published in
Acta Mathematica Scientia

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

Duong, Minh Thanh Ushirobira, Rosane
Published in
Journal of Algebra