Related papers: Constructing biquandles
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
Quandle representations are homomorphisms from a quandle to the group of invertible matrices on some vector space taken with the conjugation operation. We study certain families of quandle representations. More specifically, we introduce…
We determine the structure of automorphism group or each nonsplit metacyclic 2-group. This completes the work on automorphism groups of metacyclic $p$-groups.
We introduce the notion of mc-biquandles, algebraic structures which have possibly distinct biquandle operations at single-component and multi-component crossings. These structures provide computable homset invariants for classical and…
We give a general description of the structure of a discrete double groupoid (with an extra, quite natural, filling condition) in terms of groupoid factorizations and groupoid 2-cocycles with coefficients in abelian group bundles. Our…
We obtain analogues of classical results on automorphism groups of holomorphic fiber bundles, in the setting of group schemes. Also, we establish a lifting property of the connected automorphism group, for torsors under abelian varieties.…
We introduce new families of quandles that serve as invariants for classifying closed orientable surfaces. These families generalize the classical Dehn quandle and are defined, respectively, on isotopy classes of unoriented closed curves…
In this paper, we explore the bounded cohomology of quandles and its applications to knot theory. We establish two key results that provide sufficient conditions for the infinite dimensionality of the second bounded cohomology of quandles.…
In this paper we describe how one can obtain Lie group structures on the group of (vertical) bundle automorphisms for a locally convex principal bundle P over the compact manifold M. This is done by first considering Lie group structures on…
We define the notion of the orbit group of a quandle via its connectivity and compute the orbit groups for some basic quandles. We also show that the orbit group counts the number of orbits of certain quandles.
We consider the asymmetric orbifold that is obtained by acting with T-duality on a 4-torus, together with a shift along an extra circle. The chiral algebra of the resulting theory has non-trivial outer automorphisms that act as permutations…
We study the class of idempotent-generated pseudo-composition algebras, which is a subclass of the family of axial algebras. More specifically, we utilise the group-algebra correspondence, natural to the axial framework in order to study…
If the bimodule of 1-forms of a differential calculus over an associative algebra is the direct sum of 1-dimensional bimodules, a relation with automorphisms of the algebra shows up. This happens for some familiar quantum space calculi.
We offer a criterion for showing that the automorphism group of an ultrahomogeneous structure is topologically 2-generated and even has a cyclically dense conjugacy class. We then show how finite topological rank of the automorphism group…
Isomorphism classes of Alexander quandles of order 16 are determined, and classes of connected quandles are identified. This paper extends the list of known distinct connected finite Alexander quandles.
This paper has partially a novel and partially a survey character. We start with a short review of rack (two term) homology of self distributive algebraic structures (shelves) and their connections to knot theory. We concentrate on a…
We completely describe good involutions of free quandles and subquandles of twisted conjugation quandles of groups, including all Alexander quandles. As an application, we enumerate good involutions of linear quandles, and we provide…
We study certain subgroups of the full group of Hopf algebra automorphisms of a biproduct. In the process interesting subgroups of certain permutation groups come into play.
We describe all subdirectly irreducible medial quandles. We show that they fall within one of four disjoint classes. In particular, in the finite case they are either connected (and therefore Alexander quandles) or reductive. Moreover, we…
An adjoint Chevalley group of rank at least 2 over a rational algebra (or a similar ring), its elementary subgroup, and the corresponding Lie ring have the same automorphism group. These automorphisms are explicitly described.