Related papers: Commutative post-Lie algebra structures on Lie alg…
In this paper, the Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields are studied. Taking advantage of the Z-grading structures and the transitivity, we prove that there is only the trivial Hom-Lie…
In this paper, we introduce the notion of compatible anti-pre-Lie algebras and study relationship between them and the related structures such as anti-$\mathcal{O}$-operators, commutative $2$-cocycles on compatible Lie algebras. Moreover,…
One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra [K]. A Lie pseudoalgebra is a generalization of the…
In this paper, we characterize the biderivations of Schr\"odinger-Virasoro Lie algebra. We get a classes of non-inner and non-skewsymmetric biderivations. As application, we characterize the commutative post-Lie algebra structures on…
This paper defines the algebraic structure of tracial post-Lie-Rinehart algebras and describes the free object in this category. Post-Lie-Rinehart algebras is a generalisation of pre-Lie-Rinehart algebras, and of post-Lie algebroids.
Reductive (or semisimple) algebraic groups, Lie groups and Lie algebras have a rich geometry determined by their parabolic subgroups and subalgebras, which carry the structure of a building in the sense of J. Tits. We present herein an…
We describe transposed Poisson algebra structures on Block Lie algebras $\mathcal B(q)$ and Block Lie superalgebras $\mathcal S(q)$, where $q$ is an arbitrary complex number. Specifically, we show that the transposed Poisson structures on…
We characterize, in a purely algebraic manner, certain linear forms, called stable, on a Lie algebra. As an application, we determine the index of a Borel subalgebra of a semi-simple Lie algebra. Finally, we give an example of a parabolic…
This is a survey of results on partially commutative groups and partially commutative algebras.
It is well known that the Poisson Lie algebra is isomorphic to the Hamiltonian Lie algebra. We show that the Poisson Lie algebra can be embedded properly in the special type Lie algebra. We also generalize the Hamiltonian Lie algebra using…
Zusmanovich gave a fundamental result on the structure of $\omega$-Lie algebras. But up to now, the classification of $\omega$-Lie algebras is still open. In this paper, we give a complete classification of $\omega$-Lie algebras over…
Transposed Poisson structures on complex Galilean type Lie algebras and superalgebras are described. It was proven that all principal Galilean Lie algebras do not have non-trivial $\frac{1}{2}$-derivations and as it follows they do not…
In this paper, first we show that $(\g,[\cdot,\cdot],\alpha)$ is a hom-Lie algebra if and only if $(\Lambda \g^*,\alpha^*,d)$ is an $(\alpha^*,\alpha^*)$-differential graded commutative algebra. Then, we revisit representations of hom-Lie…
In this paper, we first introduce the concept of symmetric biderivation radicals and characteristic subalgebras of Lie algebras, and study their properties. Based on these results, we precisely determine biderivations of some Lie algebras…
In this note we further explore the properties of universal enveloping algebras associated to a post-Lie algebra. Emphasizing the role of the Magnus expansion, we analyze the properties of group like-elements belonging to (suitable…
Lie superautomorphisms of prime associative superalgebras are considered. A definitive result is obtained for central simple superalgebras: their Lie superautomorphisms are of standard forms, except when the dimension of the superalgebra in…
In this paper some results on the Lie structure of prime superalgebras are discussed. We prove that, with the exception of some special cases, for a prime superalgebra, $A$, over a ring of scalars $\Phi$ with $1/2\in \Phi$, if $L$ is a Lie…
The explicit list of all almost factorizable Lie bialgebra structures on real absolutely simple Lie algebras is given.
For a field K and directed graph E, we analyze those elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E), L_K(E)]. This analysis allows us to give easily computable necessary and sufficient conditions to…
We show that a $PL_{\infty}$-algebra $V$ can be described by a nilpotent coderivation of degree $-1$ on coalgebra $P^*V$. Based on this result, we can generalise the result of T. Lada and show that every $A_{\infty}$-algebra carries a…