Ruth Corran

Ruth Corran
American University of Paris · Computer Science, Mathematics and Environmental Science

PhD Mathematics, University of Sydney

About

13
Publications
798
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179
Citations
Additional affiliations
April 2002 - June 2004
Sorbonne University
Position
  • PostDoc Position
August 2017 - September 2017
American University of Paris
Position
  • Professor
August 2004 - August 2005
Swiss Federal Institute of Technology in Lausanne
Position
  • PostDoc Position

Publications

Publications (13)
Article
We generalize the definition and properties of root systems to complex reflection groups — roots become rank one projective modules over the ring of integers of a number field k. In the irreducible case, we provide a classification of root systems over the field of definition k of the reflection representation. In the case of spetsial reflection gr...
Article
Full-text available
We generalize the definition and properties of root systems to complex reflection groups - roots become rank one projective modules over the ring of integers of a number field k. In the irreducible case, we provide a classification of root systems over the field of definition k of the reflection representation. In the case of spetsial reflection gr...
Article
We obtain new presentations for the imprimitive complex reflection groups of type $(de,e,r)$ and their braid groups $B(de,e,r)$ for $d,r \ge 2$. Diagrams for these presentations are proposed. The presentations have much in common with Coxeter presentations of real reflection groups. They are positive and homogeneous, and give rise to quasi-Garside...
Article
Automaticity is an important concept in group theory as it yields an efficient solution to the word problem and provides other possibilities for effective computation. The concept of automaticity generalizes naturally from groups to monoids and semigroups and the efficiency of the solution of the word problem is preserved when we do this. Whilst th...
Conference Paper
Full-text available
We consider the positive singular and the singular Artin monoids of finite type. These have been the subject of a great deal of recent research and the main purpose of this paper is to prove that these monoids are automatic. In order to do this we establish a new criterion for proving monoids automatic that may be of independent interest.
Article
Full-text available
We describe a new presentation for the complex reflection groups of type (e, e, r) and their braid groups. A diagram for this presentation is proposed. The presentation is a monoid presentation that is shown to give rise to a Garside structure. This structure has since been used in understanding periodic elements, calculating homology and determini...
Article
Full-text available
We define a notion of conjugacy in singular Artin moniods, and solve the corresponding conjugacy problem for finite types. We sgiw that this definition is appropriate to describe type (1) singular Markov moves on singular braids. Parabolic submonoids of singular Artin monoids are defined and, in finite type, are shown to be singular Artin monoids....
Article
We investigate a new lattice of generalised non-crossing partitions, constructed using the geometry of the complex reflection group G(e,e,r). For the particular case e=2 (resp. r=2), our lattice coincides with the lattice of simple elements for the type Dn (resp. I2(e)) dual braid monoid. Using this lattice, we construct a Garside structure for the...
Preprint
We investigate a new lattice of generalised non-crossing partitions, constructed using the geometry of the complex reflection group $G(e,e,r)$. For the particular case $e=2$ (resp. $r=2$), our lattice coincides with the lattice of simple elements for the type $D_n$ (resp. $I_2(e)$) dual braid monoid. Using this lattice, we construct a Garside struc...
Article
Full-text available
We give a new presentation of the braid group $B$ of the complex reflection group $G(e,e,r)$ which is positive and homogeneous, and for which the generators map to reflections in the corresponding complex reflection group. We show that this presentation gives rise to a Garside structure for $B$ with Garside element a kind of generalised Coxeter ele...
Article
Full-text available
OUTLINE. In the first half of the thesis, we introduce the class of'chainable monoids' and describe general techniques for solving the word and division problems and for obtaining normal forms for monoids in this class. Their growth functions are shown to be rational, and calculable. We also show that a monoid with a certain central 'fundamental el...
Article
The first part of this paper investigates a class of homogeneously presented monoids. Constructions which enable division and multiplication to be computed are described. The word problem and the division problem are solved, and a unique normal form is given for monoids in this class. The second part deals with the motivating examples of this class...
Article
Full-text available
Introduction An Artin group is a group G with a presentation by a system of generators a i ; i 2 I, and relations a i a j a i Delta Delta Delta = a j a i a j Delta Delta Delta ; i; j 2 I where the words on each side of these relations are sequences of m ij letters where a i and a j alternate in the sequence. The matrix of values m ij is a Coxeter m...

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