The present paper is devoted to studying local derivations on the Lie algebra $W(2,2)$ which has some outer derivations. Using some linear algebra methods in \cite{CZZ} and a key construction for $W(2,2)$ we prove that every local derivation on $W(2, 2)$ is a derivation. As an application, we determine all local derivations on the deformed $\mathfrak{bms}_3$ algebra.

/pdf/local-derivations-on-the-lie-algebra-w-2-2-1vkekosr.pdf

Local derivations on the Lie algebra W(2, 2)

<jats:p>In this paper, we give a new method to classify all simple cuspidal modules for the <jats:inline-formula>
	      <jats:alternatives>
		<jats:tex-math>$\mathbb {Z}$</jats:tex-math>
		<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0308210523000203_inline1.png" />
	      </jats:alternatives>
	    </jats:inline-formula>-graded and <jats:inline-formula>
	      <jats:alternatives>
		<jats:tex-math>$1/2\mathbb {Z}$</jats:tex-math>
		<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0308210523000203_inline2.png" />
	      </jats:alternatives>
	    </jats:inline-formula>-graded Ovsienko–Roger superalgebras. Using this result, we classify all simple Harish–Chandra modules over some related Lie superalgebras, including the <jats:inline-formula>
	      <jats:alternatives>
		<jats:tex-math>$N=1$</jats:tex-math>
		<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0308210523000203_inline3.png" />
	      </jats:alternatives>
	    </jats:inline-formula> BMS<jats:inline-formula>
	      <jats:alternatives>
		<jats:tex-math>$_3$</jats:tex-math>
		<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0308210523000203_inline4.png" />
	      </jats:alternatives>
	    </jats:inline-formula> superalgebra, the super <jats:inline-formula>
	      <jats:alternatives>
		<jats:tex-math>$W(2,2)$</jats:tex-math>
		<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0308210523000203_inline5.png" />
	      </jats:alternatives>
	    </jats:inline-formula>, etc.</jats:p>

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/984A8990C45B98A43E5D72BB846C8C10/S0308210523000203a.pdf/div-class-title-classification-of-simple-harish-chandra-modules-over-the-ovsienko-roger-superalgebra-div.pdf

Classification of simple Harish–Chandra modules over the Ovsienko–Roger superalgebra

Abstract The present paper is devoted to study 2-Local derivations on the Schrödinger algebra in (2 + 1)-dimensional space-time of Schrödinger Lie groups. We prove that every 2-local derivation on this algebra is a derivation.

2-Local derivations on Schrödinger algebra in (2 + 1)- dimensional space-time

The present paper is devoted to studying local derivations on the super Virasoro algebra which is a basic object of superconformal algebras. We prove that every local derivation on the super Virasoro algebra is a derivation. As an application, we determine all local derivations on the $N=1$ super-BMS$_3$ algebra, which admits a nontrivial local derivation.

Local derivations on the super Viraosor algebra and the $N=1$ super-BMS$_3$ algebra

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 conformal Galilei algebra is a derivation.

2-local derivation on the conformal Galilei algebra

The present paper is devoted to studying 2-local superderivations on the super Virasoro algebra and the super W(2,2) algebra. It is proved that all 2-local superderivations on the super Virasoro al...

2-Local superderivations on the super Virasoro algebra and the super W(2,2) algebra

The present paper is devoted to study 2-local superderivations on the super Virasoro algebra and the super W(2,2) algebra. We prove that all 2-local superderivations on the super Virasoro algebra as well as the super W(2,2) algebra are (global) superderivations.

2-Local derivations on the Super Virasoro algebra and Super W(2,2) algebra

This paper mainly considers a class of non-weight modules over the Lie algebra of the Weyl type. First, we construct the U(h)-free modules of rank one over the differential operator algebra. Then, we characterize the tensor products of these kind of modules and the quasi-finite highest weight modules. Finally, we undertake such research for the differential operator algebra of multi-variables.

/pdf/u-h-free-modules-over-the-lie-algebras-of-differential-2ban5sns.pdf

U(h)-Free Modules over the Lie Algebras of Differential Operators

This paper is devoted to defining and studying Whittaker modules and high order Whittaker modules for the [Formula: see text] super-BMS 3 algebra. We also classify the simple Whittaker modules and obtain the necessary and sufficient conditions for the irreducibility of these modules. 

Munayim Dilxat

Papers

2-Local superderivations on the super Virasoro algebra and the super W(2,2) algebra

2-Local derivations on the Super Virasoro algebra and Super W(2,2) algebra

Classification of simple Harish–Chandra modules over the Ovsienko–Roger superalgebra

U(h)-Free Modules over the Lie Algebras of Differential Operators

Whittaker modules for the N = 1 super-BMS3 Algebra