Related papers: Quotients in supergeometry
We present two approaches, one homological and the other simplicial, for the investigation of dimension quotients of groups. The theory is illustrated, in particular, with a conceptual discussion of the fourth and fifth dimension quotients.
This article introduces patterns of ideals of numerical semigroups, thereby unifying previous definitions of patterns of numerical semigroups. Several results of general interest are proved. More precisely, this article presents results on…
Schwinger's quantization scheme is extended in order to solve the problem of the formulation of quantum mechanics on a space with a group structure. The importance of Killing vectors in a quantization scheme is showed. Usage of these…
The purpose of this paper is to study the transitive group-groupoids.
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.
We study irreducible representations of a class of quantum spheres, quotients of quantum symplectic spheres.
We outline the recent classification of differential structures for all main classes of quantum groups. We also outline the algebraic notion of `quantum manifold' and `quantum Riemannian manifold' based on quantum group principal bundles, a…
The main notions of the quantum groups: coproduct, action and coaction, representation and corepresentation are discussed using simplest examples: $GL_q(2)$, $sl_q(2)$, $q$-oscillator algebra ${\cal A}(q)$, and reflection equation algebra.…
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
I present a method of performing geometric quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UTC). I also show that by using this method…
We give an optimal necessary and sufficient condition for the quotient polynomial and remainder in the division algorithm to have positive coefficients.
The goal of this article is to emphasize the role of cubical sets in enriched categories theory and infinity-categories theory. We show in particular that categories enriched in cubical sets provide a convenient way to describe many…
In this note we examine a natural concept of a curve on a supermanifold and the subsequent notion of the jet of a curve. We then tackle the question of geometrically defining the higher order tangent bundles of a supermanifold. Finally we…
In this paper the concept of extension of a Q-fuzzy ideal in semigroups has been introduced and some important properties have been studied.
The aim of this paper is twofold. The first is to give a quantitative version of Schmidt's subspace theorem for arbitrary families of higher degree polynomials. The second is to give a generalization of the subspace theorem for arbitrary…
We describe an algorithm for computing a $\Q$-rational model for the quotient of a modular curve by an automorphism group, under mild assumptions on the curve and the automorphisms, by determining $q$-expansions for a basis of the…
This paper introduces the idea of pseudo-group. Applications of pseudo-groups in Group Theory and Symmetry Breaking in Particle Physics and Cosmology are considered.
We introduce the notion of the quotient of a category $C$ by the action $A : M \longrightarrow C \times C$ of a unital symmetric monoidal category $M$. The quotient $C/M$ is a 2-category. We prove its existence and uniqueness by first…
In this paper, we introduce the notion of a super tangent bundle of a manifold, and extend the basic notions of differential geometry such as differential forms, exterior derivation, connection, metric and divergence on manifolds that…
We consider the category of partial actions, where the group and the set upon which the group acts can vary. Within this framework, we develop a theory of quotient partial actions and prove that this category is both (co)complete and…