Related papers: Modular classes of skew algebroid relations

We introduce and characterize a particularly tractable class of unital type 1 C*-algebras with bounded dimension of irreducible representations. Algebras in this class are called recursive subhomogeneous algebras, and they have an inductive…

Let $(M,\mathcal{N})$ be a marked 3-manifold. We use $S_n(M,\mathcal{N},v)$ to denote the stated $SL_n$-skein module of $(M,\mathcal{N})$ where $v$ is a nonzero complex number. We establish a surjective algebra homomorphism from…

We begin a study of torsion theories for representations of an important class of associative algebras over a field which includes all finite W-algebras of type A, in particular the universal enveloping algebra of gl(n) (or sl(n)) for all…

Given a hyperplane arrangement in a complex vector space of dimension n, there is a natural associated arrangement of codimension k subspaces in a complex vector space of dimension k*n. Topological invariants of the complement of this…

The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},\ldots , a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}\cdots a_{n} =a_{\sigma (1)} a_{\sigma (2)} \cdots a_{\sigma (n)}$, where…

We give necessary conditions for the existence of a compact manifold locally modelled on a given homogeneous space, which generalize some earlier results, in terms of relative Lie algebra cohomology. Applications include both reductive and…

Essentially generalizing Lie's results, we prove that the contact equivalence groupoid of a class of (1+1)-dimensional generalized nonlinear Klein-Gordon equations is the first-order prolongation of its point equivalence groupoid, and then…

For a smooth quasi-projective surface S over complex numbers we consider the Borel-Moore homology of the stack of coherent sheaves on S with compact support and make this space into an associative algebra by a version of the Hall…

We prove irreducible components of moduli spaces of semistable representations of skewed-gentle algebras, and more generally, clannish algebras, are isomorphic to products of projective spaces. This is achieved by showing irreducible…

A general result relating skew monoidal structures and monads is proved. This is applied to quantum categories and bialgebroids. Ordinary categories are monads in the bicategory whose morphisms are spans between sets. Quantum categories…

Omni-Lie algebroids are generalizations of Alan Weinstein's omni-Lie algebras. A Dirac structure in an omni-Lie algebroid $\dev E\oplus \jet E$ is necessarily a Lie algebroid together with a representation on $E$. We study the geometry…

We introduce a notion of duality for a Lie-Rinehart algebra giving certain bilinear pairings in its cohomology generalizing the usual notions of Poincar\'e duality in Lie algebra cohomology and de Rham cohomology. We show that the duality…

Khovanov-Lauda-Rouquier algebras of finite Lie type come with families of standard modules, which under the Khovanov-Lauda-Rouquier categorification correspond to PBW-bases of the positive part of the corresponding quantized enveloping…

In this paper we extend and adapt several results on extensions of Lie algebras to topological Lie algebras over topological fields of characteristic zero. In particular we describe the set of equivalence classes of extensions of the Lie…

We call a finite-dimensional complex Lie algebra $\mathfrak{g}$ strongly rigid if its universal enveloping algebra $\Ug$ is rigid as an associative algebra, i.e. every formal associative deformation is equivalent to the trivial deformation.…

We associate a real distribution to any complex Lie algebroid that we call distribution of real elements and a new invariant that we call real rank, given by the pointwise rank of this distribution. When the real rank is constant, we obtain…

We classify degeneration patterns of Verma modules over the N=2 superconformal algebra in two dimensions. Explicit formulae are given for singular vectors that generate maximal submodules in each of the degenerate cases. The mappings…

This paper is about skew monoidal tensored V-categories (= skew monoidal hommed V-actegories) and their categories of modules. A module over <M,*,R> is an algebra for the monad T = R * _ on M. We study in detail the skew monoidal structure…

In this paper we construct a class of homogeneous Hilbert modules over the disc algebra $\mathcal{A}(\mathbb D)$ as quotients of certain natural modules over the function algebra $\mathcal{A}(\mathbb D^2)$. These quotient modules are…

A few steps are made towards representation theory of embeddability among uncountable graphs. A monotone class of graphs is defined by forbidding countable subgraphs, related to the graph's end-structure. Using a combinatorial theorem of…