Related papers: Structures de Weyl ALF
In Part I of this paper, we introduced a class of certain algebras of finite dimension over a field. All these algebras are split, symmetric and local. Here we continue to investigate their Loewy structure. We show that in many cases their…
These are the lecture notes based on earlier papers with some additional new results. New and simple proofs are given for local freeness theorem and the semipositivity theorem. A decomposition theorem for higher direct images of dualizing…
In this work we give a full characterization of sets of multiple polynomial recurrence in Weyl systems, which are ergodic unipotent affine transformations on products of tori and finite abelian groups. In particular, we show that measurable…
A positive mass theorem for General Relativity Theory is proved. The proof is 4-dimensional in nature, and relies completely on arguments pertaining to causal structure, the basic idea being that positive energy-density focuses null…
The problem of interpreting a set of ${\cal W}$-algebra constraints constructed in terms of an arbitrarily twisted scalar field as the recursion relations of a topological theory is addressed. In this picture, the conventional models of…
In this thesis, we attempt to gain a more complete insight into Double Layer Theories in Weyl Gravity. In order to do this, we first establish the premise of Weyls Theory, including its provenance, development and flaws. This is all…
We define global and local Weyl modules for Lie superalgebras of the form $\mathfrak{g} \otimes A$, where $A$ is an associative commutative unital $\mathbb{C}$-algebra and $\mathfrak{g}$ is a basic Lie superalgebra or $\mathfrak{sl}(n,n)$,…
Motivated by the rich geometry of conformal Riemannian manifolds and by the recent development of geometries modeled on homogeneous spaces $G/P$ with $G$ semisimple and $P$ parabolic, Weyl structures and preferred connections are introduced…
In a recent article by Farah and the authors, a strong lifting theorem was proved for a class of coordinate-respecting maps between reduced products of discrete structures, hereby working under mild Forcing Axioms. We generalise this…
We give a new formulation and proof of a theorem of Halmos and Wallen on the structure of power partial isometries on Hilbert space. We then use this theorem to give a structure theorem for a finite set of partial isometries which…
An ansatz is presented for a possible non-associative deformation of the standard Yang-Mills type gauge theories. An explicit algebraic structure for the deformed gauge symmetry is put forward and the resulting gauge theory developed. The…
We consider the general form of "Correlated Worldline" (CWL) theories of quantum gravity. We show that one can have 2 different kinds of CWL theory, in which the generating functional is written as either a sum or a product over multiple…
We show that each Weyl group which enters in the generalized Springer correspondence carries a natural weight function.
Generalized Lagrange-Weyl structures and compatible connections are introduced as a natural generalization of similar notions from Riemannian geometry. Exactly as in Riemannian case, the compatible connection is unique if certain symmetry…
In this paper, we introduce and motivate the studies of Quantum Weyl Gravity (also known as Conformal Gravity). We discuss some appealing features of this theory both on classical and quantum level. The construction of the quantum theory is…
We associate elliptic affine Lie algebras with what are called vertex $\C((z))$-algebras and their modules in a certain category. In the course, we construct two families of Lie algebras closely related to elliptic affine Lie algebras.
Given a parabolic geometry on a smooth manifold $M$, we study a natural affine bundle $A \to M$, whose smooth sections can be identified with Weyl structures for the geometry. We show that the initial parabolic geometry defines a reductive…
It is known that there exists an order isomorphism between the Weyl group orbit through a minuscule weight of a simply-laced finite-dimensional simple Lie algebra and the set of all order filters in a self-dual connected d-complete poset.…
In this paper, we prove Lorentzian positive mass theorem for spacetimes with distributional curvature. To do so, we introduce distributional curvature and generalized Arnowitt-Deser-Misner (ADM) momentum. As an application, we discuss a…
Affine Deligne-Lusztig varieties can be thought of as affine analogs of classical Deligne-Lusztig varieties, or Frobenius-twisted analogs of Schubert varieties. We provide a method for proving a non-emptiness statement for affine…