Related papers: The generalized Heisenberg-Virasoro algebra
In a recent paper by the authors, Lie bialgebra structures on generalized Heisenberg- Virasoro algebra L are considered. In this paper, the explicit formula of the quantization on generalized Heisenberg-Virasoro algebra is presented.
In this paper, Lie bialgebra structures on generalized Heisenberg-Virasoro algebra $\mathfrak{L}$ are considered. Also, $H^1({\mathfrak{L}} ,\mathfrak{L}\bigotimes\mathfrak{L})$ is given explicitly. Moreover, it is proved that all Lie…
In a recent paper by the authors, Lie bialgebras structures of generalized Virasoro-like type were considered. In this paper, the explicit formula of the quantization of generalized Virasoro-like algebras is presented.
In this paper we investigate Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra. With the classifications of Lie bialgebra structures on the Virasoro algebra, we determined such structures on the twisted Heisenberg-Virasoro…
In this paper, we study the structure theory of a class of not-finitely graded Lie algebras related to generalized Heisenberg-Virasoro algebras. In particular, the derivation algebras, the automorphism groups and the second cohomology…
In two recent papers by the authors, all Lie bialgebra structures on Lie algebras of generalized Witt type are classified. In this paper all Lie bialgebra structures on generalized Virasoro-like algebras are determined. It is proved that…
In this paper, we study the structure theory of a class of not-finitely graded Lie algebras related to generalized Virasoro algebras. In particular,the derivation algebras, the automorphism groups and the second cohomology groups of these…
In this paper, the generalized Loop Heisenberg-Virasoro algebra is introduced. Firstly, we determine the derivations on the generalized Loop Heisenberg-Virasoro algebra. Then we show that all 2-local derivations are derivations.…
This is the second paper in our series of papers dedicated to the study of the generalized loop Heisenberg-Virasoro algebra. The first paper is dedicated to the study of maps on the generalized loop Heisenberg-Virasoro algebra, including…
The first cohomology group of a generalized loop Virasoro algebra with coefficients in the tensor product of its adjoint module is shown to be trivial. The result is applied to prove that Lie bialgebra structures on generalized loop…
In this paper, by studying the maximal good subspaces, we determine the dual Lie coalgebras of the centerless twisted Heisenberg-Virasoro algebra. Based on this, we construct the dual Lie bialgebras structures of the twisted…
Generalized Virasoro algebras (defined as the universal central extension of some generalized Witt algebras) and super-Virasoro algebras and modules of the intermediate series are studied and discussed.
In this paper, we construct the Heisenberg-Virasoro algebra in the framework of the $\mathcal{R}(p,q)$-deformed quantum algebras. Moreover, the $\mathcal{R}(p,q)$-Heisenberg-Witt $n$-algebras is also investigated. Furthermore, we generalize…
Hom-Lie algebras are non-associative algebras generalizing Lie algebras by twisting the Jacobi identity by a linear map. In this paper, we mainly study the irreducible representation of the twisted Heisenberg-Virasoro algebra of Hom-type,…
2-local derivation is a generalized derivation for a Lie algebra, which plays an important role to the study of local properties of the structure of the Lie algebra. In this paper, we prove that every 2-local derivation on the twisted…
We introduce an $\mathfrak{F}$-valued generalization of the Virasoro algebra, called the Frobenius-Virasoro algebra $\mathfrak{vir_F}$, where $\mathfrak{F}$ is a Frobenius algebra over $\mathbb{R}$. We also study Euler equations on the…
We introduce and study a new class of algebras, which we name \textit{quantum generalized Heisenberg algebras} and denote by $\mathcal{H}_q (f,g)$, related to generalized Heisenberg algebras, but allowing more parameters of freedom, so as…
In this paper we investigate Lie bialgebra structures on the Schr\"odinger-Virasoro algebra $\LL$. Surprisingly, we find out an interesting fact that not all Lie bialgebra structures on the Schr\"odinger-Virasoro algebra are triangular…
This is an expository article on representation theory of toroidal Lie algebras. We summerize all the results on representation theory of toroidal Lie algebras obtained in the last fifteen years. Apart from that a natural genaralization of…
All Lie bialgebra structures on the Heisenberg--Weyl algebra $[A_+,A_-]=M$ are classified and explicitly quantized. The complete list of quantum Heisenberg--Weyl algebras so obtained includes new multiparameter deformations, most of them…