Related papers: Addendum: Weyl cocycles, (Class.Quantum Grav. 3 (1…

We calculate the Weyl anomaly for conformal field theories that can be described via the adS/CFT correspondence. This entails regularizing the gravitational part of the corresponding supergravity action in a manner consistent with general…

We review and expand upon recent work demonstrating that Weyl invariant theories can be broken "inertially," which does not depend upon a potential. This can be understood in a general way by the "current algebra" of these theories,…

This paper is concerned with the Weyl composition of symbols in large dimension. We specify a class of symbols in order to estimate the Weyl symbol of the product of two Weyl $h-$pseudodifferential operators, with constants independent of…

We provide the full classification, in arbitrary even and odd dimensions, of global conformal invariants, i.e., scalar densities in the spacetime metric and its derivatives that are invariant, possibly up to a total derivative, under local…

We show that bicovariant bimodules as defined by Woronowicz are in one to one correspondence with the Drinfeld quantum double representations. We then prove that a differential calculus associated to a bicovariant bimodule of dimension n is…

Weyl's original scale geometry of 1918 ("purely infinitesimal geometry") was withdrawn by its author from physical theorizing in the early 1920s. It had a comeback in the last third of the 20th century in different contexts: scalar tensor…

In this work we consider all metric Lie algebras, having a nondegenerate symmetric invariant bilinear form, over \C and \R up to dimension 5 and all metric Lie algebras over \C in dimension 6. We introduce cyclic and reduced cyclic…

This article is devoted to rational equivalence for non-commutative polynomial algebras in a context including both the classical Gelfand-Kirillov problem and its quantum version. We introduce in this ``mixed'' context some reference…

Two differential calculi are developped on an algebra generalizing the usual q-oscillator algebra and involving three generators and three parameters. They are shown to be invariant under the same quantum group that is extended to a…

We classify up to isomorphism the quantum generalized Weyl algebras and determine their automorphism groups in all cases in a uniform way, including those where the parameter q is a root of unity, thereby completing the results obtained by…

The behavior of the divergent part of the bulk AdS/CFT effective action is considered with respect to the special finite diffeomorphism transformations acting on the boundary as a Weyl transformation of the boundary metric. The resulting…

Let W be a Weyl group and let w be a Coxeter elememt of minimal length of W. In the early 1970's I.G.Macdonald stated that the trace of w on an irreducible representation of W is 0,1 or -1. In this paper we give a proof of this statement…

A Weyl geometric scale covariant approach to gravity due to Omote, Dirac, and Utiyama (1971ff) is reconsidered. It can be extended to the electroweak sector of elementary particle fields, taking into account their basic scaling freedom.…

In this note, we evaluate the Weyl-invariant quadratic curvature tensors for the particular Weyl's gauge field constructed in the $3+1$-dimensional noncompact Weyl-Einstein-Yang-Mills model. We subsequently extend the model to its higher…

The evolution of 4-dimensional and (4+d)-dimensional (d=1,2) cosmological models based on the integrable Weyl geometry are considered numerically both for empty space-time and for scalar field with non minimal coupling with gravity.

In this paper we study metric deformations of indecomposable metric Lie superalgebras with dimensions less or equal to 6. We consider formal deformations obtained by even cocycles, because the odd ones can not be used for constructing…

Weyl conformal geometry is a gauge theory of scale invariance that naturally brings together the Standard Model (SM) and Einstein gravity. The SM embedding in this geometry is possible without new degrees of freedom beyond SM and Weyl…

In recent work (math.QA/0309252) on multivariate hypergeometric integrals, the author generalized a conjectural integral formula of van Diejen and Spiridonov to a ten parameter integral provably invariant under an action of the Weyl group…

We calculate the integrated trace anomaly for a real spin-0 scalar field in six dimensions in a torsionless curved space without a boundary. We use a path integral approach for a corresponding supersymmetric quantum mechanical model. Weyl…

The most general lagrangian describing spin 2 particles in flat spacetime and containing operators up to (mass) dimension 6 is carefully analyzed, determining the precise conditions for it to be invariant under linearized (transverse)…