Related papers: Lifting multiplicative lattices to ideal sytems
We obtain an algorithmic construction of the isotropy lattice for a lifted action of a Lie group $G$ on $TM$ and $T^*M$ based only on the knowledge of $G$ and its action on $M$. Some applications to symplectic geometry are also shown.
Liftings of endofunctors on sets to endofunctors on relations are commonly used to capture bisimulation of coalgebras. Lax versions have been used in those cases where strict lifting fails to capture bisimilarity, as well as in modeling…
We describe new methods for deciding the stability of switching systems. The methods build on two ideas previously appeared in the literature: the polytope norm iterative construction, and the lifting procedure. Moreover, the combination of…
We present a procedure to improve the lattice definition of $\mathcal N = 4$ supersymmetric Yang--Mills theory. The lattice construction necessarily involves U(1) flat directions, and we show how these can be lifted without violating the…
Some years ago, Borcherds described in [Bo1] two methods for constructing modular forms on modular varieties related to the orthogonal group ${\O}(2,n)$. They are the so called Borcherds' additive and multiplicative lifting. The…
The goal of this paper is to deepen the study of multiplicative lattices in the sense of Facchini, Finocchiaro and Janelidze. We provide a sort of Prime Ideal Principle that guarantees that maximal implies prime in a variety of cases (among…
For a minimal inequality derived from a maximal lattice-free simplicial polytope in $\R^n$, we investigate the region where minimal liftings are uniquely defined, and we characterize when this region covers $\R^n$. We then use this…
We study the multiplicative lattices L which satisfy the condition a = (a : (a : b))(a : b) for all a,b in L.
Many polytopes arising in polyhedral combinatorics are linear projections of higher-dimensional polytopes with significantly fewer facets. Such lifts may yield compressed representations of polytopes, which are typically used to construct…
Let $\widehat{\mathscr O}$ be a complete local principal ideal ring with residue field $k$ of characteristic not $2$ and $f\in \widehat{\mathscr O}[x_1,x_2,\dots,x_m]$. Take $A\in \mathrm M_n(\widehat{\mathscr O})$ with its reduction…
We discuss the possibility of representing supersymmetry exactly in a lattice discretized system. In particular, we construct a perfect supersymmetric action for the Wess-Zumino model.
In this article, we present a new algorithm for computing a generating set of a lattice ideal. This algorithm is based on a project-and-lift approach and is implemented in 4ti2. We also include a computational comparison of several existing…
There exist several theorems which state that when a matroid is representable over distinct fields F_1,...,F_k, it is also representable over other fields. We prove a theorem, the Lift Theorem, that implies many of these results. First,…
We determine a new technique which allows the computation of the arithmetical rank of certain monomial ideals.
We describe an equivalent formulation of algebraic weak factorisation systems, not involving monads and comonads, but involving double categories of morphisms equipped with a lifting operation satisfying lifting and factorisation axioms.
We introduce a method to lift monads on the base category of a fibration to its total category. This method, which we call codensity lifting, is applicable to various fibrations which were not supported by its precursor, categorical…
It is well known that a matroid L is a lift of a matroid M if and only if every circuit of L is the union of some circuits of M. In this paper we give a simpler proof of this important theorem. We also described a discrete homotopy theorem…
Lifting methods allow to transform hard variational problems such as segmentation and optical flow estimation into convex problems in a suitable higher-dimensional space. The lifted models can then be efficiently solved to a global optimum,…
We present a method of constructing symmetric monoidal bicategories from symmetric monoidal double categories that satisfy a lifting condition. Such symmetric monoidal double categories frequently occur in nature, so the method is widely…
We characterize numerical semigroups for which the poset of its ideal class monoid is a lattice, and study the irreducible elements of such a lattice with respect to union, intersection, infimum and supremum.