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In this essay, we immerse into the framework of normed division algebras as a suitable arena to accommodate the standard model of elementary particles, and we explore some applications to cosmology. Remarkably, they permit interesting…
We describe the ternary and the generalized superderivations of finite-dimensional semisimple Jordan superalgebras over an algebraically closed field of characteristic zero and of finite-dimensional simple Jordan superalgebras with…
Examples are presented for appearance of geometric symmetry in the shape of various astronomical objects and phenomena. Usage of these symmetries in astrophysical and extragalactic research is also discussed.
We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other.
I contrast the profound differences in the ways in which algebra and analysis are used in physics. In particular I discuss the fascinating phenomenon that theoretical physicists devote almost all their efforts to algebraic problems even…
We survey some algebraic geometric aspects of mirror symmetry and duality in string theory. Some applications of computer algebra to algebraic geometry and string theory are shortly reviewed.
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
Necessary and sufficient conditions for some deformation algebras to provide formal Frobenius structures are given. Also, examples of formal Frobenius structures with fundamental tensor that is not of the deformation type and examples of…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
Semi-entwining structures are proposed as concepts simpler than entwining structures, yet they are shown to have interesting applications in constructing intertwining operators and braided algebras, lifting functors, finding solutions for…
In an earlier work extensions of supersymmetry and super Lie algebras were constructed consistently starting from any representation $\D$ of any Lie algebra $\g$. Here it is shown how infinite dimensional Lie algebras appear naturally…
This is part two of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1- Alphabetical bibliography, 2- Analytical bibliography, 3- Notations and terminology, and 4- Formulas and…
Supersymmetry has been studied for over three decades by physicists, its superset even longer by mathematicians, and superspace has proven to be very useful both conceptually and in facilitating computations. However, the (1) necessary…
These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in…
The algebraic structure on the subspace of the quasi-primary vectors given by the projection of the (n) products of a conformal superalgebra is formulated. As an application the complete list of simple physical conformal superalgebras is…
We show that each irreducible tensor representation of weight 2 of the rotation group of three-dimensional space in the space of rank 3 covariant tensors gives rise to an associative algebra with unity. We find the algebraic relations that…
A cell algebra structure is found for a family of generalized Schur algebras previously studied by the author. This cell algebra structure is then used to construct the irreducible representations of these algebras and to determine when the…
The central structure in various versions of noncommutative geometry is a differential calculus on an associative algebra. This is an analogue of the calculus of differential forms on a manifold. In this short review we collect examples of…
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.