Partial symmetry, reflection monoids and Coxeter groups

Brent Everitt; John Fountain

doi:10.1016/j.aim.2009.10.008

Partial symmetry, reflection monoids and Coxeter groups

Brent Everitt, John Fountain

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection monoids, introduce new examples, and determine their orders. (C) 2009 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	1782-1814
Number of pages	33
Journal	Advances in Mathematics
Volume	223
Issue number	5
DOIs	https://doi.org/10.1016/j.aim.2009.10.008
Publication status	Published - 20 Mar 2010

Keywords

Coxeter groups
Hyperplane arrangements
Inverse semigroups
Algebraic monoids
Renner monoids
UNIFORM BLOCK PERMUTATIONS
ALGEBRAIC MONOIDS
RENNER MONOIDS
BRUHAT DECOMPOSITION
ARRANGEMENTS

Access to Document

10.1016/j.aim.2009.10.008

http://www.sciencedirect.com/science/article/pii/S0001870809003235

Cite this

@article{bdbbec7107574d8bac632632a82276f8,

title = "Partial symmetry, reflection monoids and Coxeter groups",

abstract = "This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection monoids, introduce new examples, and determine their orders. (C) 2009 Elsevier Inc. All rights reserved.",

keywords = "Coxeter groups, Hyperplane arrangements, Inverse semigroups, Algebraic monoids, Renner monoids, UNIFORM BLOCK PERMUTATIONS, ALGEBRAIC MONOIDS, RENNER MONOIDS, BRUHAT DECOMPOSITION, ARRANGEMENTS",

author = "Brent Everitt and John Fountain",

year = "2010",

month = mar,

day = "20",

doi = "10.1016/j.aim.2009.10.008",

language = "English",

volume = "223",

pages = "1782--1814",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press",

number = "5",

}

TY - JOUR

T1 - Partial symmetry, reflection monoids and Coxeter groups

AU - Everitt, Brent

AU - Fountain, John

PY - 2010/3/20

Y1 - 2010/3/20

N2 - This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection monoids, introduce new examples, and determine their orders. (C) 2009 Elsevier Inc. All rights reserved.

AB - This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection monoids, introduce new examples, and determine their orders. (C) 2009 Elsevier Inc. All rights reserved.

KW - Coxeter groups

KW - Hyperplane arrangements

KW - Inverse semigroups

KW - Algebraic monoids

KW - Renner monoids

KW - UNIFORM BLOCK PERMUTATIONS

KW - ALGEBRAIC MONOIDS

KW - RENNER MONOIDS

KW - BRUHAT DECOMPOSITION

KW - ARRANGEMENTS

UR - http://www.scopus.com/inward/record.url?scp=75149172888&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2009.10.008

DO - 10.1016/j.aim.2009.10.008

M3 - Article

SN - 0001-8708

VL - 223

SP - 1782

EP - 1814

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 5

ER -

Partial symmetry, reflection monoids and Coxeter groups

Abstract

Keywords

Access to Document

Other files and links

Cite this