Related papers: Graded modules for Virasoro-like algebra
In this paper, we construct a family of non-weight modules over the super-Virasoro algebras. Those modules when regarded as modules of the Ramond algebra and further restricted as modules over the Cartan subalgebra $\mathfrak{h}$ are free…
In this paper, we give a complete classification of extensions of finite irreducible conformal modules over rank two Lie conformal algebras.
It is shown that there are no simple mixed modules over the twisted N=1 Schr\"{o}dinger-Neveu-Schwarz algebra, which implies that every irreducible weight module over it with a nontrivial finite-dimensional weight space, is a Harish-Chandra…
For a smooth irreducible affine algebraic variety we study a class of gauge modules admitting compatible actions of both the algebra $A$ of functions and the Lie algebra $\mathcal{V}$ of vector fields on the variety. We prove that a gauge…
Assume $A$ is weakly symmetric, indecomposable, with radical cube zero and radical square non-zero. We show that such algebra of wild representation type does not have a non-projective module $M$ whose ext algebra is finite-dimensional.…
We introduce the notion of the $\infty$-category of (complete) derived $G$-graded modules over a $G$-graded ring $R$ for a torsion-free abelian group $G$, and we study its foundational properties. Moreover, we prove a categorical…
Lie conformal algebras $\mathcal{W}(a,b)$ are the semi-direct sums of Virasoro Lie conformal algebra and its nontrivial conformal modules of rank one. In this paper, we give a complete classification of extensions of finite irreducible…
We define a family of universal finite-dimensional highest weight modules for affine Lie algebras, we call these Weyl modules. We conjecture that these are the classical limits of the irreducible finite--dimensional representations of the…
The main result of the paper establishes the irreducibility of a large family of nonzero central charge induced modules over Affine Lie algebras for any non standard parabolic subalgebra. It generalizes all previously known partial results…
We prove that any unitary highest weight module over a universal minimal quantum affine $W$-algebra at non-critical level descends to its simple quotient. We find the defining relations of the unitary simple minimal quantum affine…
The irreducible integrable representations with finite-dimensional weight spaces of toroidal Lie algebras on which the center acts non-trivially were classified by S.Eswara Rao. In this paper we give a compact proof of the results that lead…
We classify all irreducible highest-weight unitary modules over the non-compact real form $\mathfrak{u}(p,q|n)$ of the general linear Lie superalgebra $\mathfrak{gl}_{p+q|n}$. The classification is given by explicit necessary and sufficient…
In this paper we study graded Bourbaki ideals. It is a well-known fact that for torsionfree modules over Noetherian normal domains, Bourbaki sequences exist. We give criteria in terms of certain attached matrices for a homomorphism of…
The study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory. In this paper we consider the general set-up of a vertex algebra $V$, graded by $\G/\Z$ for some…
In this paper, we study modules for the Twisted Full Toroidal Lie Algebras (TFTLA). We define a category of bounded modules for TFTLA and classify all the irreducible modules in that category. A class of irreducible bounded modules are…
We investigate representations of the $\mathbb{Z}_2^2$-graded extension of $osp(1|2)$ which is the spectrum generating algebra of the recently introduced $\mathbb{Z}_2^2$-graded version of superconformal mechanics. The main result is a…
A general notion of a quasi-finite algebra is introduced as an algebra graded by the set of all integers equipped with topologies on the homogeneous subspaces satisfying certain properties. An analogue of the regular bimodule is introduced…
It is well known that the ring radical theory can be approached via language of modules. In this work, we present some generalizations of classical results from module theory, in the two-sided and graded sense. Let $\mathsf{G}$ be a group,…
In this paper, we consider irreducible quasi-finite (or equivalently weakly integrable) modules, with non-trivial action of the core, over the extended affine Lie algebras (EALAs) whose centerless cores are multiloop algebras. The…
Let M(1) be the vertex algebra for a single free boson. We classify irreducible modules of certain vertex subalgebras of M(1) generated by two generators. These subalgebras correspond to the W(2, 2p-1)--algebras with central charge $1- 6…