Generalized superderivations of the super Virasoro algebras
We explicitly determine the generalized superderivations of the Neveu-Schwarz and Ramond algebras.
math.RA↗
arXiv subjects
Dashu Xu
Publications and source records attributed to Dashu Xu.
Simple $\mathcal{W}\ltimes\widehat{H_4}$-modules from tensor products
This paper investigates simple modules of the semi-direct product algebra $\mathcal{W}\ltimes\widehat{H_4}$, where $\mathcal{W}$ is the Witt algebra and $\widehat{H_4}$ is the loop Diamond algebra. We first use simple modules over the Weyl algebra to construct a family of simple $\mathcal{W}\ltimes\widehat{H_4}$-modules. Then, we classify simple $\mathcal{W}\ltimes\widehat{H_4}$-modules that are free $U(\mathbb{C}L_0\oplus\mathbb{C} a_0)$-modules of rank 1. Finally, we give a necessary and sufficient condition for finitely many simple $U(\mathbb{C}L_0\oplus\mathbb{C}a_0)$-free modules to be simple, and then determine their isomorphism classes.
math.RT↗
Simple modules of the planar Galilean conformal algebra from tensor products
This paper is devoted to constructing simple modules of the planar Galilean conformal algebra. We study the tensor products of finitely many simple $\mathcal{U}(\mathcal{H})$-free modules with an arbitrary simple restricted module, where $\mathcal{H}$ is the Cartan subalgebra. We establish necessary and sufficient conditions for simplicity and determine the corresponding isomorphism classes.
math.RT↗
Simple restricted modules of non-zero level over a deformed Heisenberg-Virasoro algebra
We study representations of a deformed Heisenberg-Virasoro algebra that does not admit a triangular decomposition. Despite this, its $\mathbb{Z}$-gradation allows the classification of simple restricted modules. We show that all such modules of non-zero level arise via induction from simple modules of finite-dimensional solvable Lie algebras.
math.RT↗
New simple modules for the $W$-algebra $W(2,2)$
In this paper, we construct a novel class of simple modules for the $W$-algebra $W(2,2)$. Our approach involves taking tensor products of finitely many non-weight simple modules $\Omega(\lambda,\alpha,h)$ with an arbitrary simple restricted module. We provide a necessary and sufficient condition for these modules to be simple, and subsequently determine their isomorphism classes. Through a comparative analysis with other known simple modules in the literature, we establish that these constructed modules are generically new.
math.RT↗
Radicals of weight one blocks of Ariki-Koike algebras
Let $K$ be a field and $q\in K$, $q\neq 0, 1$. Let $\mathcal {H}_n(q, Q)$ be an Ariki-Koike algebra, where the cyclotomic parameter $Q=(Q_1, Q_2, \cdots, Q_r)\in K^r$ with $r\geq 2$, $Q_i=q^{a_i}$, $a_i\in \mathbb{Z}$. For a weight one block $B$ of $\mathcal {H}_n(q, Q)$, we prove in this paper that $\text{rad}\:B=I$, where $I$ is the nilpotent ideal constructed for a symmetric cellular algebra in [Radicals of symmetric cellular algebras, Colloq. Math. {\bf 133} (2013) 67-83]. We also give some applications of this result.
math.RA↗