Related papers: Division Algebras and Wireless Communication
Let S be a symbol algebra. The trace form of S is computed and it is shown how this form can be used to determine whether S is a division algebra or not. In addition, the exterior powers of the trace form of S are computed.
A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating…
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)…
Hom-quadri dendriform algebras and Hom-six-dendriform agebras are introduced and studied which is a splitting of a Hom-diassociative and Hom-triassociative algebras, respectively. Moreover we explore the connections be tween these…
This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…
After a self-contained introduction to Lie algebra cohomology, we present some recent applications in mathematics and in physics. Contents: 1. Preliminaries: L_X, i_X, d 2. Elementary differential geometry on Lie groups 3. Lie algebra…
In the last quarter of a century, algebraic statistics has established itself as an expanding field which uses multilinear algebra, commutative algebra, computational algebra, geometry, and combinatorics to tackle problems in mathematical…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
Doppler effect is a fundamental phenomenon that appears in wave propagation, where a moving observer experiences dilation or contraction of wavelength of a wave. It also appears in radio frequency (RF) wireless communication when there…
This paper addresses some aspects of the general problem of information transfer and distributed function computation in wireless networks. Many applications of wireless technology foresee networks of autonomous devices executing tasks that…
In this paper, we introduce some new classes of algebras related to UP-algebras and semigroups, called a left UP-semigroup, a right UP-semigroup, a fully UP-semigroup, a left-left UP-semigroup, a right-left UP-semigroup, a left-right…
The concept of integro-differential algebra has been introduced recently in the study of boundary problems of differential equations. We generalize this concept to that of integro-differential algebra with a weight, in analogy to the…
We obtain a complete classification of minimal simple unitary $W$-algebras.
This paper provides a comprehensive survey on recent advances in deep learning (DL) techniques for the channel coding problems. Inspired by the recent successes of DL in a variety of research domains, its applications to the physical layer…
Recent advances in wideband impulse technology, low power communication along with unlicensed band have enabled ultra wide band (UWB) as a leading technology for future wireless applications. This paper outlines the applications of emerging…
I present here some new results which make explicit the role of the division algebras R,C,H,O in the construction and classification of, respectively, N=1,2,4,8 global supersymmetric quantum mechanical and classical dynamical systems. In…
We define a new cohomology for associative algebras which we compute for algebras with units.
A customary solution to reduce the energy consumption of wireless communication devices is to periodically put the radio into low-power sleep mode. A relevant problem is to schedule the wake-up of nodes in such a way as to ensure proper…
The link of the Division Algebras to 10-dimensional spacetime and one leptoquark family is extended to 26-dimensional spacetime and three leptoquark families.
We study the dual algebras of (discrete) Hopf algebroids. In particular, we understand comodules over a Hopf algebroid as (discrete) modules over its dual algebra.