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In this paper, a family of non-weight modules over Lie superalgebras $S(q)$ of Block type are studied. Free $U(eta)$-modules of rank $1$ over Ramond-Block algebras and free $U(mathfrak{h})$-modules of rank $2$ over Neveu-Schwarz-Block algebras are constructed and classified. Moreover, the sufficient and necessary conditions for such modules to be simple are presented, and their isomorphism classes are also determined. The results cover some existing results.
We classify all simple bounded highest weight modules of a basic classical Lie superalgebra $mathfrak g$. In particular, our classification leads to the classification of the simple weight modules with finite weight multiplicities over all classical
We prove that the tensor product of a simple and a finite dimensional $mathfrak{sl}_n$-module has finite type socle. This is applied to reduce classification of simple $mathfrak{q}(n)$-supermodules to that of simple $mathfrak{sl}_n$-modules. Rough st
Let ${mathcal W}_n$ be the Lie algebra of polynomial vector fields. We classify simple weight ${mathcal W}_n$-modules $M$ with finite weight multiplicities. We prove that every such nontrivial module $M$ is either a tensor module or the unique simple
This paper aims to describe the restricted Kac modules of restricted Hamiltonian Lie superalgebras of odd type over an algebraically closed field of characteristic $p>3$. In particular, a sufficient and necessary condition for the restricted Kac modu
We construct a class of non-weight modules over the twisted $N=2$ superconformal algebra $T$. Let $mathfrak{h}=C L_0oplusC G_0$ be the Cartan subalgebra of $T$, and let $mathfrak{t}=C L_0$ be the Cartan subalgebra of even part $T_{bar 0}$. These modu