Related papers: An Algorithm to Construct A Basis for the Module o…
We analyse the algebras generated by free component quantum fields together with the susy generators $Q,\bar Q$. Restricting to hermitian fields we first construct the scalar field algebra from which various scalar superfields can be…
Hyperplane arrangements form the latest addition to the zoo of combinatorial objects dealt with by polymake. We report on their implementation and on a algorithm to compute the associated cell decomposition. The implemented algorithm…
By a codimension-one system we mean a system whose lattice of relations has rank one. We consider codimension-one $A$-hypergeometric systems and explicitly construct some of the logarithmic series solutions at the origin. When the parameter…
We study the combinatorics of hyperplane arrangements over arbitrary fields. Specifically, we determine in which situation an arrangement and its reduction modulo a prime number have isomorphic lattices via the use of minimal strong…
It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous…
In this survey paper, we review recent work on frameworks for the high-level, portable programming of heterogeneous multi-/manycore systems (especially, GPU-based systems) using high-level constructs such as annotated user-level software…
We represent vector bundles over a regular algebraic curve as pairs of lattices over the maximal orders of its function field and we give polynomial time algorithms for several tasks: computing determinants of vector bundles, kernels and…
The vector field problem is an important and classical problem in differential topology. In this survey we shall consider the vector field problem focusing mainly on the class of compact homogeneous spaces.
Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum…
We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the…
We introduce a weighted version of the module of logarithmic derivations of a divisor in weighted projective space, and provide a generalization of Saito's criterion for freeness in terms of weighted multiple eigenschemes (wME-schemes).…
We define the field $\mathbb{L}$ of logarithmic hyperseries, construct on $\mathbb{L}$ natural operations of differentiation, integration, and composition, establish the basic properties of these operations, and characterize these…
We introduce the concept of a graded bundle which is a natural generalization of the concept of a vector bundle and whose standard examples are higher tangent bundles T^nQ playing a fundamental role in higher order Lagrangian formalisms.…
We introduce a new class of arrangements of hyperplanes, called (strictly) plus-one generated arrangements, from algebraic point of view. Plus-one generatedness is close to freeness, i.e., plus-one generated arrangements have their…
We construct an algorithm for the minimal model program in dimension three over the field of algebraic numbers. As auxiliary results, we also construct algorithms for computing bigraded global Hom modules and for computing Stein…
We quantize homogeneous vector bundles over an even complex sphere $\mathbb{S}^{2n}$ as one-sided projective modules over its quantized coordinate ring. We realize them in two different ways: as locally finite $\mathbb{C}$-homs between…
This paper computes the bases of the image of $2$-adic logarithm on the group of the principal units in all 7 quadratic extensions of $\mathbb{Q}_2$. This helps one to understand the free module structure of $2$-adic logarithm at arbitrary…
Given a finite residue field $k$, one looks for a smoothness basis that is invariant under the automorphism group of $k$. We construct models for some finite fields that admit such a basis. This work aims at accelerating algorithms for…
We develop an elementary method to compute spaces of equivariant maps from a homogeneous space $G/H$ of a Lie group $G$ to a module of this group. The Lie group is not required to be compact. More generally, we study spaces of invariant…
We use the theory of hyperplane arrangements to construct natural bases for the homology of partition lattices of types A, B and D. This extends and explains the "splitting basis" for the homology of the partition lattice given in [Wa96],…