Related papers: Listening to Celestial Algebras
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
Sujets qui sont plus particulierement abordes dans ce cours: 1. Elements de cosmologie, l'Univers homogene Les principes cosmologiques et leurs verifications observationnelles Histoire thermique de l'Univers Inflation, motivations et…
For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…
The manner in which one approaches the interface between gravitation and quantum theory is influenced by one's posture regarding quantum mechanics and the issues that revolve about its interpretational problems. We discuss here the way in…
The aim of these lecture notes is to familiarize graduate students and beginning postgraduates with the basic ideas of linear cosmological perturbation theory and of structure formation scenarios. We present both the Newtonian and the…
Linear algebra is usually defined over a field such as the reals or complex numbers. It is possible to extend this to skew fields such as the quaternions. However, to the authors' knowledge there is no commonly accepted notation of linear…
We generalize Albert's twisted field construction, applying it to unital division algebras with a multiplicative norm. We give conditions for the resulting algebras to be division algebras.Four- and eight-dimensional real unital and…
Spherical manifolds yield cosmic spaces with positive curvature. They result by closing pieces from the sphere used by Einstein for his initial cosmology. Harmonic analysis on the manifolds aims at explaining the observed low amplitudes at…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
This lecture is an introduction to cosmological tests with clusters of galaxies. Here I do not intend to provide a complete review of the subject, but rather to describe the basic procedures to set up the fitting machinery to constrain…
Cosmic strings are predicted in many models beyond the Standard Model of particle physics. In models which admit strings, a network of strings will inevitably be formed in a phase transition in the early universe and will persist to the…
These lecture notes for the 2013 CIME/CIRM summer school Combinatorial Algebraic Geometry deal with manifestly infinite-dimensional algebraic varieties with large symmetry groups. So large, in fact, that subvarieties stable under those…
In this paper we lay down the foundations for a purely Newtonian theory of cosmology, valid at scales small compared with the Hubble radius, using only Newtonian point particles acted on by gravity and a possible cosmological term. We…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
Given the wealth of increasingly accurate cosmological observations, especially the recent results from the WMAP, and the development of methods and strategies in the search for cosmic topology, it is reasonable to expect that we should be…
We discuss the potential cosmological role of gravitational wave astronomy as a probe of the very early universe. The next generation of detectors - now in production - may be able to observe a stochastic background of gravitational waves…
The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By…
With WMAP putting the phenomenological standard model of cosmology on a strong footing, one can look forward to mining the cosmic microwave background (CMB) for fundamental physics with higher sensitivity and on smaller scales. Future CMB…
Reframing certain well-known particle models in terms of normed division algebras leads to two new results for BSM physics. (1) We identify a sequence of complex structures which induces a cascade of breaking symmetries: Spin(10) $\mapsto$…
Forthcoming cosmic microwave background experiments (CMB) will provide precise new tests of structure-formation theories. The geometry of the Universe may be determined robustly, and the classical cosmological parameters, such as the…