Related papers: Higher rank Bell--Rogalski algebras

We generalize fundamental notions of higher algebra, traditionally developed within the $\infty$-category of spectra, to the broader setting of $t$-structured tensor triangulated $\infty$-categories ($ttt$-$\infty$-categories). Under a…

For any finitely generated abelian group $Q$, we reduce the problem of classification of $Q$-graded simple Lie algebras over an algebraically closed field of "good" characteristic to the problem of classification of gradings on simple Lie…

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…

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…

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…

This is the first part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. This theory generalizes the tensor category theory for…

We investigate the algebraic structure of integrable hierarchies that, we propose, underlie models of $W$-gravity coupled to matter. More precisely, we concentrate on the dispersionless limit of the topological subclass of such theories, by…

Reductions of higher tangent bundles of Lie groupoids provide natural examples of geometric structures which we would like to call higher algebroids. Such objects can be also constructed abstractly starting from an arbitrary almost Lie…

Criterion of (Shilov) regularity for weighted algebras $L_1^w(G)$ on a locally compact abelian group $G$ is known by works of Beurling (1949) and Domar (1956). In the present paper this criterion is extended to translation invariant…

We construct explicit bases of simple modules and Bernstein-Gelfand-Gelfand (BGG) resolutions of all simple modules of the (graded) Temperley-Lieb algebra of type B over a field of characteristic zero.

Each connected graded, graded-commutative algebra $A$ of finite type over a field $\Bbbk$ of characteristic zero defines a complex of finitely generated, graded modules over a symmetric algebra, whose homology graded modules are called the…

We describe a logarithmic tensor product theory for certain module categories for a ``conformal vertex algebra.'' In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not…

The loop algebra construction by Allison, Berman, Faulkner, and Pianzola, describes graded-central-simple algebras with split centroid in terms of central simple algebras graded by a quotient of the original grading group. Here the…

We introduce analogues of Soergel bimodules for complex reflection groups of rank one. We give an explicit parametrization of the indecomposable objects of the resulting category and give a presentation of its split Grothendieck ring by…

Generalized Weyl Algebras (GWAs) appear in diverse areas of mathematics including mathematical physics, noncommutative algebra, and representation theory. We study the invariants of quantum GWAs under finite automorphisms. We extend a…

In this article, a large class of simple modules over the Schr\"odinger-Virasoro algebra $\mathcal{G}$ are constructed, which include highest weight modules and Whittaker modules. These modules are determined by the simple modules over the…

We define analogues of Verma modules for finite W-algebras. By the usual ideas of highest weight theory, this is a first step towards the classification of finite dimensional irreducible modules. Motivated by known results in type A, we…

The Bershadsky--Polyakov algebras are the subregular quantum hamiltonian reductions of the affine vertex operator algebras associated with $\mathfrak{sl}_3$. In arXiv:2007.00396 [math.QA], we realised these algebras in terms of the regular…

We introduce a generalization of the notion of a Koszul algebra, which includes graded algebras with relations in different degrees, and we establish some of the basic properties of these algebras. This class is closed under twists, twisted…

It is proved that for a vector space W, any set of parafermion-like vertex operators on W in a certain canonical way generates a generalized vertex algebra in the sense of [DL2] with W as a natural module. This result generalizes a result…