Related papers: Smarandache Multi-Space Theory(I)-Algebraic multi-…
We describe spinors in Minkowskian spaces with arbitrary signature and their role in the classification of space-time superalgebras and their R-symmetries in any dimension.
The dimensional structure of space-time is investigated according to physical and mathematical methods. We show that ther are various empirical and theoretical restrictions on the number of independent dimensions of space-time, consequently…
In this article we show that $\mathbb{S}/8$ is an $\mathbb{E}_1$-algebra, $\mathbb{S}/32$ is an $\mathbb{E}_2$-algebra, $\mathbb{S}/p^{n+1}$ is an $\mathbb{E}_n$-algebra at odd primes and, more generally, for every $h$ and $n$ there exist…
A dilatation structure is a concept in between a group and a differential structure. In this article we study fundamental properties of dilatation structures on metric spaces. This is a part of a series of papers which show that such a…
A manifestly Lorentz-covariant calculus based on two matrix-coordinates and their associated derivatives is introduced. It allows formulating relativistic field theories in any even-dimensional spacetime. The construction extends a…
A non-elementary M\"obius group generated by two-parabolics is determined up to conjugation by one complex parameter and the parameter space has been extensively studied. In this paper, we use the results of \cite{GW} to obtain an…
In this paper, the module-algebra structures of $U_q(sl(m+1))$ on the quantum $n$-space $A_q(n)$ are studied. We characterize all module-algebra structures of $U_q(sl(m+1))$ on $A_q(2)$ and $A_q(3)$ when $m\geq 2$. The module-algebra…
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
Generalising the definition to commuting $d$-tuples of operators, a number of authors have considered structural properties of $m$-isometric, $n$-symmetric and $(m,n)$-isosymmetric commuting $d$-tuples in the recent past. This note is an…
This is the first in a series of papers in which we describe explicit structural properties of spaces of diagonal rectangular harmonic polynomials in $k$ sets of $n$ variables, both as $GL_k$-modules and $S_n$-modules, as well as some of…
The relation between open topological strings and representation theory of symmetric quivers is explored beyond the original setting of the knot-quiver correspondence. Multiple cover generalizations of the skein relation for boundaries of…
A global superalgebra with 32 supercharges and all possible central extensions is studied in order to extract some general properties of duality and hidden dimensions in a theory that treats $p$-branes democratically. The maximal number of…
We begin the investigation of the variety of semilattices of Mal'cev blocks, which we call SMB algebras.
The paper examines machines of the type of the $\Gamma$-spaces of Segal which describe homotopy structures on topological spaces. The main result of the paper shows that for any such machine one can find an algebraic theory characterizing…
We describe all metric spaces that have sufficently many affine functions. As an application we obtain a metric characterization of linear-convex subsets of Banach spaces.
We abstract and generalize homotopical monadicity statements, placing in a single conceptual framework a range of old and recent recognition and characterization principles in iterated loop space theory in classical, equivariant, and…
A brief review of the harmonic superspace approach to the construction of $\mathcal{N}=2$ supersymmetric higher spin theories is given. We define off-shell analytic harmonic gauge potentials of $\mathcal{N}=2$ supersymmetric higher-spin…
A Lambda (Card Lambda > aleph)-product space of {0,1} has a partition {X1,...,Xn} for any n a decomposition space of each Xi of which is self-similar.(February 16, 2015)
This is the first of a two-part work on Kleiman's iterated multiple point spaces. We show general properties of these spaces, leading to explicit equations describing them for maps (of any corank) between complex manifolds. We also describe…
Processes are often viewed as coalgebras, with the structure maps specifying the state transitions. In the simplest case, the state spaces are discrete, and the structure map simply takes each state to the next states. But the coalgebraic…