相关论文: Januarials of simple and general type
This is an account of a series of lectures of Graham Higman on "januarials", namely coset graphs for actions of triangle groups which become 2-face maps when embedded in orientable surfaces.
Professor Graham Higman defined januarial as a special instance of map constructed from embedding of a coset diagram for an action of $\Delta (2,\ell ,k)$, on finite sets yielding exactly two orbits of the product of the two generators,…
It is widely written and believed that Edwin Hubble introduced the terms `early' and `late types' to suggest an evolutionary sequence for galaxies. This is incorrect. Hubble took these terms from spectral classification of stars to signify…
We describe the generic $\sigma$-conjugacy classes associated with the Iwahori-Bruhat decomposition of a reductive group. As an application, we classify cordial elements as introduced by Mili\'cevi\'c-Viehmann.
The theory of categories of fractions as originally developed by Gabriel and Zisman is reviewed in a pedagogical manner giving detailed proofs of all statements. A weakening of the category of fractions axioms used by Higson is discussed…
We propose elementary and explicit presentations of groups that have no amenable quotients and yet are SQ-universal. Examples include groups with a finite classifying space, no Kazhdan subgroups and no Haagerup quotients.
In this survey article we introduce the notion of frontals, which provides a class of generalised submanifolds with singularities but with well-defined tangent spaces. We present a review of basic theory and known studies on frontals in…
We present here definitions and constructions basic for the theory of monoidal and tensor categories. We provide references to the original sources, whenever possible. Group-theoretical categories are used as examples
Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here. Axiomatizations are provided for three successively more general classes of causal models: (1) the class of recursive theories (those…
Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here. Axiomatizations are provided for three successively more general classes of causal models: (1) the class of recursive theories (those…
We introduce formal languages over infinite alphabets where words may contain binders. We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata)…
We developed a type-theoretical framework for natural lan- guage semantics that, in addition to the usual Montagovian treatment of compositional semantics, includes a treatment of some phenomena of lex- ical semantic: coercions, meaning,…
D. G. Higman generalized a coherent configuration and defined a weight. In this article, we will modify the definition and investigate weights on coherent configurations. If our weights are on a thin homogeneous coherent configuration, that…
An unresolved conjecture by Graham Higman states that for all $n\geq 1$ the number of conjugacy classes of the group of $n \times n$ unitriangular matrices with entries in the finite field $\mathbb{F}_q$ is a polynomial in $q$. In this…
In this informal introduction to dg categories, the slogan is that dg categories are more rudimentary than triangulated categories. We recall some details on the dg quotient category introduced by Bernhard Keller and Vladimir Drinfeld.
We introduce the notion of a hierarchical quandle, which is a generalisation of diquandles and multi-quandles. Using hierarchical quandle colourings, we construct a cocycle invariants for links coloured by quandles.
We first prove that, for any generalized Hamiltonian type Lie algebra $L$, the first cohomology group $H^1(L,L \otimes L)$ is trivial. We then show that all Lie bialgebra structures on $L$ are triangular.
We provide a complete classification of all algebras of generalised dihedral type, which are natural generalizations of algebras which occurred in the study of blocks with dihedral defect groups. This gives a description by quivers and…
Using random variables as motivation, this paper presents an exposition of the formalisms developed by Rota and Taylor for the classical umbral calculus. A variety of examples are presented, culminating in several descriptions of sequences…
Many different types of fractional calculus have been defined, which may be categorised into broad classes according to their properties and behaviours. Two types that have been much studied in the literature are the Hadamard-type…