We classify regular subalgebras of affine Kac–Moody algebras in terms of their root systems. In the process, we establish that a root system of a subalgebra is always an intersection of the root system of the algebra with a sublattice of its root lattice. We also discuss applications to investigations of regular subalgebras of hyperbolic Kac–Moody algebras and conformally invariant subalgebras ...

In this paper, we look at long geometric progressions on diferent model of elliptic curves, namely Weierstrass curves, Edwards and twisted Edwards curves, Huf curves and general quartics curves. By a geometric progression on an elliptic curve, we mean the existence of rational points on the curve whose x-coordinate (or y-coordinate) are in geometric progression. We fnd infnite families of twist...

Heterotic string models in which the space-time gauge symmetry is realized as a level k > 2 Kac-Moody algebra on the string world-sheet offer phenomenological features not present for the level k = 1 case (which includes all heterotic string models seriously considered to date). In particular, string models with N=l space-time supersymmetry and/or chiral matter fields can contain massless scala...

The first presenter, Professor Mariana Mazzucato (University of Sussex, UK), spoke about EU innovation policy in relation to risk taking and obtaining the return, and she challenged the common, but false, assumption that the public sector has a limited role in economic growth and innovation. The second presenter, technology writer Glyn Moody, focused on equitable licensing, open-source research...

We will show the Gauss decomposition with prescribed torus elements for a Kac-Moody group over a field in general case.

Moody's endorses the Basel Committee's proposal to use banks' internal risk assessments to re®ne the Basel Accord's risk weights on bank assets and commitments. External risk assessments, such as Moody's credit ratings, will likely play a supporting role as direct inputs into banks' internal rating systems and as tools for benchmarking and validating those systems. However, the widespread use o...