Related papers: Loop torsors. Theory and applications
The main perpose of this paper is to sudy the roots of a familly of polynomials that arise from a linear recurrences associated to Pascal's triangle and their zero attractor, using an analytical methods based on conformal mappings.
A skew Laurent polynomial ring R[x^{\pm 1};\alpha] is reversible if it has a reversing automorphism, that is, an automorphism of period two that transposes x and x^{-1} and restricts to an automorphism of R. We study invariants for…
We consider a category of modules that admit compatible actions of the commutative algebra of Laurent polynomials and the Lie algebra of divergence zero vector fields on a torus and have a weight decomposition with finite dimensional weight…
Let $E$ be an elliptic curve, defined over a quartic extension $K$ of $\mathbb{Q}$, with $j(E) \in \mathbb{Q}$. In this paper, we classify the possible torsion subgroup structures $E(K)_{\text{tors}}$.
We study the relative modular classes of Lie algebroids, and we determine their relationship with the modular classes of Lie algebroids with a twisted Poisson structure.
Following a recent proposal for integrable theories in higher dimensions based on zero curvature, new Lorentz invariant submodels of the principal chiral model in 2+1 dimensions are found. They have infinite local conserved currents, which…
In his proof of the fundamental lemma, Ng\^o established the product formula for the Hitchin fibration over the anisotropic locus. One expects this formula over the larger generically regular semisimple locus, and we confirm this by…
We relate the author's Lie cobracket in the module additively generated by loops on a surface with the Connes-Kreimer Lie bracket in the module additively generated by trees. To this end we introduce a pre-Lie coalgebra and a (commutative)…
This work is devoted to the study of the support of a Laurent series in several variables which is algebraic over the ring of power series over a characteristic zero field. Our first result is the existence of a kind of maximal dual cone of…
This paper focuses on the theory of the Hecke rings associated with the general linear groups originally studied by Hecke and Shimura et al., and moreover generalizes its notions to Hecke rings associated with the automorphism groups of…
We study the relationship between multiplicative 2-forms on Lie groupoids and linear 2-forms on Lie algebroids, which leads to a new approach to the infinitesimal description of multiplicative 2-forms and to the integration of twisted Dirac…
For several objects of interest in geometric complexity theory, namely for the determinant, the permanent, the product of variables, the power sum, the unit tensor, and the matrix multiplication tensor, we introduce and study a fundamental…
We give a brief introduction to computational algebraic number theory in OSCAR. Our main focus is on number fields, rings of integers and their invariants. After recalling some classical results and their constructive counterparts, we…
By analogy with the definition of group with triality we introduce Lie algebra with triality as Lie algebra L wich admits the group of automorphisms S_3={s,r | s^2=r^3=1, srs=r^2} such that for any x\in L we have…
This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader…
Recent developments on emergence of logarithmic terms in correlators or response functions of models which exhibit dynamical symmetries analogous to conformal invariance in not necessarily relativistic systems are reviewed. The main…
Twisted K-theory has received much attention recently in both mathematics and physics. We describe some models of twisted K-theory, both topological and geometric. Then we state a theorem which relates representations of loop groups to…
The Galois theory of logarithmic differential equations with respect to relative D-groups in partial differential-algebraic geometry is developed.
We develop a theory of commensurability of groups, of rings, and of modules. It allows us, in certain cases, to compare sizes of automorphism groups of modules, even when those are infinite. This work is motivated by the Cohen-Lenstra…
Loop braid groups characterize the exchange of extended objects, namely loops, in three dimensional space generalizing the notion of braid groups that describe the exchange of point particles in two dimensional space. Their interest in…