Related papers: The Geometry of Nim
We generalise the notions of supersymmetry and superspace by allowing generators and coordinates transforming according to more general Lorentz representations than the spinorial and vectorial ones of standard lore. This yields novel…
This paper analyses the Noether symmetries and the corresponding conservation laws for Chern-Simons Lagrangians in dimension $d=3$. In particular, we find an expression for the superpotential of Chern-Simons gravity. As a by-product the…
We study higher dimensional counterparts to the well-known theorem of Pavlovic \cite{pa3}, that every harmonic quasiconformal mapping of the disk is bi-Lipschitz.
Non-orientable nanostructures are becoming feasable today. This lead us to the study of spin in these geometries. Hence a physically sound definition of spin is suggested. Using our definition, we study the question of the number of…
This paper first introduces a new generalized inverse in Minkowski space, called the m-DMP inverse, and discusses its algebraic and geometrical properties. The second objective is to characterize the m-DMP inverse equivalently by ranges,…
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…
We initiate the study of non- and ultra-relativistic higher spin theories. For sake of simplicity we focus on the spin-3 case in three dimensions. We classify all kinematical algebras that can be obtained by all possible In\"on\"u--Wigner…
In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.
A framework for discussing relationships between different types of games is proposed. Within the framework, quantum simultaneous games, finite quantum simultaneous games, quantum sequential games, and finite quantum sequential games are…
Nim is a well-known combinatorial game in which two players alternately remove stones from distinct piles. A player who removes the last stone wins under the normal play rule, while a player loses under the mis\`ere play rule. In this…
We investigate various aspects of higher-spin anti-de Sitter supergravity in three dimensions as described by Chern-Simons theory based on the finite-dimensional superalgebra sl(N |N - 1), with the particular case of N = 3 as our prime…
For any ring we propose the construction of a cover which increases the finitistic dimension on one side and decreases the finitistic dimension to zero on the opposite side. This complements recent work of Cummings.
We introduce perfect half space games, in which the goal of Player 2 is to make the sums of encountered multi-dimensional weights diverge in a direction which is consistent with a chosen sequence of perfect half spaces (chosen dynamically…
We consider a generalization of the notion of a natural mechanical system to the case of additional forces of gyroscopic type. Such forces appear, for example, as a result of global reduction of a natural system with symmetry. We study…
We define the notion of dextral symmetric algebras (not necessarily associative), motivated by the idea of symmetric rings. We derive a complete classification of dextral symmetric algebras of Leavitt path algebras, and right Leibniz…
If we label the vertices of a triangle with 1, 2 and 4, and the orthocentre with 7, then any of the four numbers 1, 2, 4, 7 is the nim-sum of the other three and is their orthocentre. Regard the triangle as an orthocentric quadrangle.…
We introduce a geometric property complementary-finite asymptotic dimension (coas- dim). Similar with asymptotic dimension, we prove the corresponding coarse invariant theorem, union theorem and Hurewicz-type theorem.
In the paper we apply some of the results from the theory of ball spaces in the semimetric spaces. This allowed us to obtain some fixed point theorems which we believe to be unknown to this day. We also show the limitations of the ball…
We characterize countable dimensionality and strong countable dimensionality by means of an infinite game.
Bielavsky introduced and investigated the class of symmetric symplectic spaces, that is, symmetric spaces endowed with a symplectic form invariant with respect to symmetries. Since the theory of symmetric spaces has generalizations, we ask…