Related papers: Listening to Celestial Algebras
We investigate the prospects for probing asymmetric dark matter models through their gravitational wave signatures. We concentrate on a theory extending the Standard Model gauge symmetry by a non-Abelian group, under which leptons form…
We argue that once octonions are formulated as soft Lie algebras, they may be safely used and the non-associativity can be overcame. The necessary points are: (a) Fixing the direction of action by introducing the \delta operator. (b)…
We explore the capability of deep learning to classify cosmic structures. In cosmological simulations, cosmic volumes are segmented into voids, sheets, filaments and knots, according to the distribution and kinematics of dark matter (DM),…
Assuming a fractal distribution of matter in the universe, consequences that follow from the General Theory of Relativity and the Copernican Principle for fractal cosmology are examined. The change in perspective necessary to deal with a…
We study not necessarily associative (NNA) division algebras over the reals. We classify in this paper series those that admit a grading over a finite group $G$, and have a basis $\{v_g|g\in G\}$ as a real vector space, and the product of…
We consider the class of algebras of rank 4 equipped with a standard involution over an arbitrary base ring. In particular, we characterize quaternion rings, those algebras defined by the construction of the even Clifford algebra.
In recent years, there is a growing interest in the studying octonions, which are 8-dimensional hypercomplex numbers forming the biggest normed division algebras over the real numbers. In particular, various tools of the classical complex…
I discuss, through a few examples, how observational cosmology can provide insights on hypothetical fundamental physics phenomena or mechanisms, such as Grand Unified Theory, Superstring alternatives to the inflation paradigm, and inflation…
Chiral tetrahedral molecules can be dealt under the standard of quaternionic algebra. Specifically, non-commutativity of quaternions is a feature directly related to the chirality of molecules. It is shown that a quaternionic representation…
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
We consider theories of gravity that include many coupled scalar fields with arbitrary couplings, in the geometric framework of wave maps. We examine the possibility of obtaining acceptable cosmological solutions without the inclusion of a…
The observation of primordial gravitational waves could provide a new and unique window on the earliest moments in the history of the universe, and on possible new physics at energies many orders of magnitude beyond those accessible at…
By consireding representation theory for non-associative algebras we construct the fundamental and adjoint representations of the octonion algebra. We then show how these representations by associative matrices allow a consistent octonionic…
Several assumptions at the foundation of the standard cosmological model have as a direct consequence a specific relation between cosmological distances, known as the distance duality relation, whose violation would be a smoking gun of…
In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…
Axial algebras are a recently introduced class of non-associative algebra motivated by applications to groups and vertex-operator algebras. We develop the structure theory of axial algebras focussing on two major topics: (1) radical and…
Celestial scattering amplitudes for massless particles are Mellin transforms of momentum-space scattering amplitudes with respect to the energies of the external particles, and behave as conformal correlators on the celestial sphere.…
We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the…
In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. We define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with…
I will review some results of observational cosmology which critically cast doubt upon the foundations of the standard cosmology: 1) The redshifts of the galaxies are due to the expansion of the Universe; 2) The cosmic microwave background…