Related papers: Extensions of inertial blocks
We extend to nilpotent orbits the notion of chiral Hecke algebra introduced by Beilinson-Drinfeld. Upon analysing their isotypic components, we produce many new modules over simple affine vertex algebras at non-admissible integer levels, as…
This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian…
A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.
We extend a result due to Kawai on block varieties for blocks with abelian defect groups to blocks with arbitrary defect groups. This partially answers a question by J. Rickard.
In this note we will present an extension of the Krein-Rutman theorem for an abstract nonlinear, compact, positively 1-homogeneous, monotone non-decreasing operators on a Banach space and apply the result to many nonlinear elliptic partial…
New definitions of rack and quandle modules are introduced, and shown to generalise the definitions previously studied by Andruskiewitsch, Etingof and Grana. This new construct is shown to coincide with Beck's general definition of a module…
We extend the infinitesimal Torelli theorem for smooth hypersurfaces to nodal hypersurfaces.
We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.
Some quantum algebras build from deformed oscillator algebras may be described in terms of a particular case of extended umbral calculus. We give here an example of a specific relation between such certain quantum algebras and generalized…
This is a first paper of a series in which we give some generalizations of the Obukhov theorem in the Tucker-Wang approach to Metric- Affine gravity in which we consider more general actions containing scalar and in general fields which do…
Partial Isometries are important constructs that help give nontrivial solutions once a simple solution is known. We generalize this notion to Extended Partial Isometries and include operators which have right inverses but no left inverses…
Let $k$ be a field of characteristic $0$, $X$ be a geometrically connected, smooth and proper variety over $k$ and $x\in X(k)$ be a base point. Using the notion of iterated universal extensions, we show that Nori's fundamental group…
A basis of quasi-invariant module over invariants is explicitly constructed for the two-dimensional Coxeter systems with arbitrary multiplicities. It is proved that this basis consists of $m$-harmonic polynomials, thus the earlier results…
We introduce a broader class of nonassociative Ore extensions that unifies and generalizes several earlier constructions. We prove generalizations of Hilbert's Basis Theorem for this class, showing that they arise immediately from the…
The construction of HNN-extensions of involutive Hom-associative algebras and involutive Hom-Lie algebras is described. Then, as an application of HNN-extension, by using the validity of Poincar\'e-Birkhoff-Witt theorem for involutive…
In this paper we study the Kummer extensions of the power series field $K=k((X_1,...,X_n)$, where $k$ is an algebraically closed field of arbitrary characteristic.
We describe the equivariant K-groups of a family of generalized Steinberg varieties that interpolates between the Steinberg variety of a reductive, complex algebraic group and its nilpotent cone in terms of the extended affine Hecke algebra…
We describe the structure of ``K-approximate subgroups'' of torsion-free nilpotent groups, paying particular attention to Lie groups. Three other works, by Fisher-Katz-Peng, Sanders and Tao, have appeared which independently address related…
We point out that some of the proposed generalized/modified uncertainty principles originate from solvable, or nilpotent at appropriate limits, "deformations" of Lie algebras. We briefly comment on formal aspects related to the…
We consider the structure of groups and algebras that can be represented as automorphisms or derivations of distributive products -- which includes nonassociative rings, modules, forms, and commutation of groups and nonassociative loops. In…