Related papers: Dimension quotients
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…
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…
The purpose of this paper is to present the notion of quotient of supergroups in different categories using the unified treatment of the functor of points and to examine some physically interesting examples.
We introduce three notions of partial bihamiltonian structures ($\operatorname{PQ}$, $\operatorname{PN}$ et $\operatorname{P\Omega}$) in the convenient setting defined by Fr\"{o}licher, Kriegl and Michor. We study geometrical objects linked…
This article is an introductory work to a larger research project devoted to pure, applied and philosophical aspects of dimension theory. It concerns a novel approach toward an alternate dimension theory foundation: the point-dimension…
Dimension theory lies at the heart of fractal geometry and concerns the rigorous quantification of how large a subset of a metric space is. There are many notions of dimension to consider, and part of the richness of the subject is in…
For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in the literature. We extend these results…
One could begin a study like the present one by simply postulating that our universe is four-dimensional. There are ample reasons for doing this. Experience, observation and experiment all point to the fact that we inhabit a…
We study quotients of projective and affine spaces by various actions of the icosahedral group. Basically we concentrate on the rationality questions.
This thesis discusses various aspects of duality in quantum field theory and string theory. In the first part we consider duality in topological quantum field theories, concentrating on the Donaldson and Seiberg-Witten theories as (dual)…
We define two notions of discrete dimension based on the Minkowski and Hausdorff dimensions in the continuous setting. After proving some basic results illustrating these definitions, we apply this machinery to the study of connections…
We construct a family of heptagon relations -- algebraic imitations of five-dimensional Pachner move 3--4, parameterized by simplicial 3-cocycles.
For every $n\geq 1$, we calculate the Hochschild homology of the quantum monoids $M_q(n)$, and the quantum groups $GL_q(n)$ and $SL_q(n)$ with coefficients in a 1-dimensional module coming from a modular pair in involution.
A new homological dimension is introduced to measure the quality of resolutions of `singular' finite dimensional algebras (of infinite global dimension) by `regular' ones (of finite global dimension). Upper bounds are established in terms…
We are going to introduce a new algebraic, analytic structure that is a kind of generalization of the Hausdorff dimension and measure. We give many examples and study the basic properties and relations of such systems.
A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…
Since the 5D canonical metric embeds all 4D vacuum solutions of Einstein's equations, I review its application to the cosmological 'constant', quantized particles, deBroglie waves, scalar fields and wave-particle duality. There are several…
In this paper we shall give formulas for the pairings of intersection cohomology classes of complementary dimensions in the intersection cohomology of geometric invariant theoretic quotients for which semistability is not necessarily the…
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…