Related papers: On Core Quandles
The notion of a flag kernel on a homogeneous group is exteded to distributions of arbitrary multidimensional order. It is shown that under natural restrictions on order the operation of convolution admits an extension to thus generalised…
We find surface subgroups in certain one-relator groups with torsion and use this to deduce a profinite criterion for a word in the free group to be primitive.
In this paper we characterize smooth complex projective varieties that admit a quadric bundle structure on some dense open subset in terms of the geometry of certain families of rational curves.
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
Our ongoing work aims at defining an ontology-centered approach for building expertise models for the CommonKADS methodology. This approach (which we have named "OntoKADS") is founded on a core problem-solving ontology which distinguishes…
Let X be an irreducible, primitive complex character of the finite solvable group G, and let X* denote the complex conjugate character. If the degree X(1) is odd, then we show how to associate to X in a unique way, a conjugacy class of…
We present different ways of endowing a particular category of graphs with Quillen model structures. We show, among other things, that the core of a graph can be seen as its homotopy type in an appropriate Quillen model structure, and that…
This preprint specifies quality requirements for a core ontology whose ontological elements such as terms, non-taxonomic relationships, among others, are based on a foundational ontology. The quality requirements are represented in a…
A basis for the space of generalized theta functions of level one for the spin groups, parameterized by the theta characteristics (the even theta characteristcs for the odd spin groups) on a curve, is shown to be projectively flat over the…
In this paper we characterize the projective modules over an arbitrary quantale, and then we apply such a characterization in order to define the K_0 group of a quantale. Then we study congruences of quantales and quantale modules by means…
This article uses basic homological methods for evaluating examples of compactly supported cohomology groups of line bundles over projective curve.
We show that the fundamental quandle defines a functor from the oriented tangle category to a suitably defined quandle category. Given a tangle decomposition of a link $L$, the fundamental quandle of $L$ may be obtained from the fundamental…
The goal of this paper is to characterization generalized Alexander quandles of finite groups in the language of the underlying groups. Firstly, we prove that if finite groups $G$ are simple, then the quandle isomorphic classes of…
We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and…
We show that the structure of a fibered knot, as a fiber bundle, is reflected in its knot quandle. As an application, we discuss finiteness and equivalence of knot quandles of concrete fibered 2-knots.
We present some variations on some of the main open problems on character degrees. We collect some of the methods that have proven to be very useful to work on these problems. These methods are also useful to solve certain problems on zeros…
Quandles are certain algebraic structures showing up in different mathematical contexts. A group $G$ with the conjugation operation forms a quandle, $\operatorname{Conj}(G)$. In the opposite direction, one can construct a group…
We present simple graph-theoretic characterizations of Cayley graphs for monoids, semigroups and groups. We extend these characterizations to commutative monoids, semilattices, and abelian groups.
The axioms of a quandle imply that the columns of its Cayley table are permutations. This paper studies quandles with exactly one non-trivially permuted column. Their automorphism groups, quandle polynomials, (symmetric) cohomology groups,…
A quandle is an algebraic structure which attempts to generalize group conjugation. These structures have been studied extensively due to their connections with knot theory, algebraic combinatorics, and other fields. In this work, we…