For the BMS-Kac-Moody algebra, tensor products of finitely many U(h)-free modules with an irreducible restricted module are irreducible exactly when the lambda parameters are pairwise distinct, and the isomorphism class is determined by the original data.
New simple modules for the $W$-algebra $W(2,2)$
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abstract
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.
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A new class of irreducible modules over the BMS-Kac-Moody algebra
For the BMS-Kac-Moody algebra, tensor products of finitely many U(h)-free modules with an irreducible restricted module are irreducible exactly when the lambda parameters are pairwise distinct, and the isomorphism class is determined by the original data.