6 citations · 18 across the 24 of their papers we have counts for
31 papers
A universal characteristic class for vector bundles with a connection
Helge Øystein Maakestad
In the paper I introduce a new characteristic class for a finite rank vector bundle on an affine scheme - the fundamental class of . The class is…
A refined Weyl character formula for comodules on
Helge Øystein Maakestad
Let be any commutative unital ring and let be the general linear group scheme on of rank . We study the representation theory of $\operatorname…
A universal Clebsch-Gordan filtration for
Helge Öystein Maakestad
The aim of the paper is to study the group schemes and universal Clebsch-Gordan filtrations. Here is a field or any commu…
Conjectures on L-functions for flag bundles on Dedekind domains
Helge Øystein Maakestad
Let be the ring of integers in an algebraic number field and let . Let be regular schemes of finite type…
Classification of Lie algebras of differential operators
Helge Øystein Maakestad
In a previous paper we introduced the notion of a D-Lie algebra . A D-Lie algebra is an -Lie-Rinehart algebra with a right -module structure and a ca…
On the birational invariance of the arithmetic genus and Euler characteristic
Helge Øystein Maakestad
The aim of this note is to use elementary methods to give a large class of examples of projective varieties over a field with the property that $Y…
The enveloping algebra of a Lie algebra of differential operators
Helge Øystein Maakestad
The aim of this note is to prove various general properties of a generalization of the full module of first order differential operators on a commutative ring - a $\operatorname{D}…
Extensions of Lie algebras of differential operators
Helge Øystein Maakestad
The aim of this note is to introduce the notion of a -Lie algebra and to prove some elementary properties of -Lie algebras, the category of $\op…
Algebraic connections on projective modules with prescribed curvature
Helge Øystein Maakestad
In this paper we generalize classical results on Lie algebras and universal enveloping algebras of Lie algebras to Lie-Rinehart algebras. We define for any Lie-Rinehart algebra …
Explicit formulas for algebraic connections on ellipsoid surfaces
Helge Øystein Maakestad
The aim of this paper is to give a new method to construct explicit formulas for algebraic differential operators of any order on a finitely generated projective module on a co…
Jet bundles on projective space: New examples
Helge Øystein Maakestad
In previous papers it was shown that the left and right O-module structure of the jet bundles on the projective line differed. In this paper we show that similar statements hold fo…
Higher order differential operators on projective modules
Helge Øystein Maakestad
In this paper we give explicit formulas for higher order differential operators on a finitely generated projective module on an arbitrary commutative unital ring . We use th…
Scalar generalized Verma modules
Helge Øystein Maakestad
In this paper we study the scalar generalized Verma module associated to a character of a parabolic subgroup of . Here is a finite dimensional vector…
On jets, extensions and characteristic classes II
Helge Øystein Maakestad
In this paper we define and study generalized Atiyah classes for quasi coherent sheaves relative to arbitrary morphisms of schemes. We use derivations and quasi coherent sheaves of…
On discriminants and incidence resolutions
Helge Øystein Maakestad
In this paper we study the incidence complex of an arbitrary morphism of locally free sheaves relative to an arbitrary quasi compact morphism of schemes. We prove it is a local com…
On the canonical filtration of an irreducible representation
Helge Øystein Maakestad
The aim of this paper is to study the canonical filtration of an irreducible finite dimensional -module using the universal enveloping algebra…
Jet bundles on projective space II
Helge Øystein Maakestad
Let G=SL(E) be the special linear algebraic group on E where E is a finite dimensional vector space over a field K of characteristic zero. In this paper we study the canonical filt…
Discriminants of morphisms of sheaves
Helge Øystein Maakestad
The aim of this paper is to give a unified definition of a large class of discriminants arising in algebraic geometry using the discriminant of a morphism of locally free sheaves.…
On jets, extensions and characteristic classes I
Helge Øystein Maakestad
In this paper we give general definitions of non-commutative jets in the local and global situation using square zero extensions and derivations. We study the functors Exank(A, I)…
On jet bundles and generalized Verma modules II
Helge Øystein Maakestad
Let G be a semi simple linear algebraic group over a field of characteristic zero and let V be a finite dimensional irreducible G-module with highest weight vector v. Let P in G be…
On jet bundles and generalized Verma modules
Helge Øystein Maakestad
The aim of this paper is to initiate a study of the jet bundles on the grassmannian over a field of characteristic zero using higher direct images of -linearized sheaves, Li…
On operations and characteristic classes
Helge Øystein Maakestad
In this paper exterior products are used to define operations and characteristic classes with values in the K-theory of an abelian category with tensor and exterior products. We ap…
Notes on the Chern-character
Helge Øystein Maakestad
Notes for some talks given at the seminar on characteristic classes at NTNU in autumn 2006. In the paper a proof of the existence of a Chern-character from complex K-theory to any…
Gauss-Manin connections and Lie-Rinehart cohomology
Helge Maakestad
In this note a generalized Gauss-Manin connection is constructed for cohomology of Lie-Rinehart algebras, generalizing the classical Gauss-Manin connection. As an application a Gys…