Ordering Garside groups

2019 ◽  
Vol 29 (05) ◽  
pp. 861-883
Author(s):  
Diego Arcis ◽  
Luis Paris
Keyword(s):  
Artin Groups ◽  
Type Formula ◽  
Left Order

We introduce a structure on a Garside group that we call Dehornoy structure and we show that an iteration of such a structure leads to a left-order on the group. We define two conditions on a Garside group [Formula: see text] and we show that if [Formula: see text] satisfies these two conditions, then [Formula: see text] has a Dehornoy structure. Then, we show that the Artin groups of type [Formula: see text] and of type [Formula: see text], [Formula: see text] satisfy these conditions, and therefore have Dehornoy structures. As indicated by the terminology, one of the orders obtained by this method on the Artin groups of type [Formula: see text] coincides with the Dehornoy order.

scholarly journals PALINDROMES AND ORDERINGS IN ARTIN GROUPS

2010 ◽  
Vol 19 (02) ◽  
pp. 145-162 ◽  
Author(s):  
FLORIAN DELOUP
Keyword(s):  
Finite Type ◽  
Braid Group ◽  
Type A ◽  
Reverse Order ◽  
Artin Groups ◽  
Left Order ◽  
Group B ◽  
Half Twist

The braid group Bn, endowed with Artin's presentation, admits two distinguished involutions. One is the anti-automorphism rev : Bn →Bn, [Formula: see text], defined by reading braids in the reverse order (from right to left instead of left to right). Another one is the conjugation τ : x ↦ Δ-1xΔ by the generalized half-twist (Garside element). More generally, the involution rev is defined for all Artin groups (equipped with Artin's presentation) and the involution τ is defined for all Artin groups of finite type. A palindrome is an element invariant under rev. We study palindromes and palindromes invariant under τ in Artin groups of finite type. Our main results are the injectivity of the map [Formula: see text] in all finite-type Artin groups, the existence of a left-order compatible with rev for Artin groups of type A, B, D, and the existence of a decomposition for general palindromes. The uniqueness of the latter decomposition requires that the Artin groups carry a left-order.

scholarly journals Verlinde formulae on complex surfaces: K-theoretic invariants

2021 ◽  
Vol 9 ◽  
Author(s):  
L. Göttsche ◽  
M. Kool ◽  
R. A. Williams
Keyword(s):  
Moduli Space ◽  
K3 Surfaces ◽  
Complex Surfaces ◽  
Type Formula ◽  
Verlinde Formula ◽  
Donaldson Invariants

Abstract We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between K-theoretic Donaldson invariants studied by Göttsche and Nakajima-Yoshioka and K-theoretic Vafa-Witten invariants introduced by Thomas and also studied by Göttsche and Kool. We verify our conjectures in many examples (for example, on K3 surfaces).

scholarly journals A Class of Integral Operators that Fix Exponential Functions

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini ◽  
Gumrah Uysal ◽  
Basar Yilmaz
Keyword(s):  
General Class ◽  
Pointwise Convergence ◽  
Type Theorem ◽  
Integral Operators ◽  
Exponential Functions ◽  
Convergence Theorems ◽  
Korovkin Type Theorem ◽  
Type Formula

AbstractIn this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified operators of Gauss–Weierstrass, or Picard or moment type operators. Pointwise convergence theorems are studied, using a Korovkin-type theorem and a Voronovskaja-type formula is obtained.

scholarly journals Graphical splittings of Artin kernels

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Enrique Miguel Barquinero ◽  
Lorenzo Ruffoni ◽  
Kaidi Ye
Keyword(s):  
Free Group ◽  
Artin Group ◽  
Artin Groups ◽  
Graphs Of Groups ◽  
Underlying Graph ◽  
Block Graphs ◽  
Right Angled Artin Groups

Abstract We study Artin kernels, i.e. kernels of discrete characters of right-angled Artin groups, and we show that they decompose as graphs of groups in a way that can be explicitly computed from the underlying graph. When the underlying graph is chordal, we show that every such subgroup either surjects to an infinitely generated free group or is a generalized Baumslag–Solitar group of variable rank. In particular, for block graphs (e.g. trees), we obtain an explicit rank formula and discuss some features of the space of fibrations of the associated right-angled Artin group.

scholarly journals Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

2021 ◽  
Author(s):  
Andreas Bernig ◽  
Dmitry Faifman ◽  
Gil Solanes
Keyword(s):  
Riemannian Manifolds ◽  
Riemannian Geometry ◽  
Riemannian Space ◽  
Space Forms ◽  
Type Formula ◽  
Isometric Embeddings ◽  
Curvature Measures ◽  
Riemannian Space Forms

AbstractThe recently introduced Lipschitz–Killing curvature measures on pseudo-Riemannian manifolds satisfy a Weyl principle, i.e. are invariant under isometric embeddings. We show that they are uniquely characterized by this property. We apply this characterization to prove a Künneth-type formula for Lipschitz–Killing curvature measures, and to classify the invariant generalized valuations and curvature measures on all isotropic pseudo-Riemannian space forms.

SPACE-CHARGE LAYER, INTRINSIC "BULK" AND SURFACE COMPLEX DEFECTS IN ZnO NANOPARTICLES — A HIGH-FIELD ELECTRON PARAMAGNETIC RESONANCE ANALYSIS

2013 ◽  
Vol 06 (04) ◽  
pp. 1330004 ◽  
Author(s):  
RÜDIGER-A. EICHEL ◽  
EMRE ERDEM ◽  
PETER JAKES ◽  
ANDREW OZAROWSKI ◽  
JOHAN VAN TOL ◽  
...  
Keyword(s):  
Electron Paramagnetic Resonance ◽  
Space Charge ◽  
Zno Nanoparticles ◽  
High Field ◽  
Space Charge Layer ◽  
Paramagnetic Resonance ◽  
Charge Layer ◽  
Type Formula ◽  
Field Electron ◽  
Electron Paramagnetic

The defect structure of ZnO nanoparticles is characterized by means of high-field electron paramagnetic resonance (EPR) spectroscopy. Different point and complex defects could be identified, located at the "bulk" or the surface region of the nanoparticles. In particular, by exploiting the enhanced g-value resolution at a Larmor frequency of 406.4 GHz, it could be shown that the resonance commonly observed at g = 1.96 is comprised of several overlapping resonances from different defects. Based on the high-field EPR analysis, the development of a space-charge layer could be monitored that consists of (shallow) donor-type [Formula: see text] defects at the "bulk" and acceptor-type [Formula: see text] and complex [Formula: see text] defects at the surface. Application of a core-shell model allows to determine the thickness of the depletion layer to 1.0 nm for the here studied compounds [J.J. Schneider et al., Chem. Mater.22, 2203 (2010)].

scholarly journals The BNS-invariant for some Artin groups of arbitrary circuit rank

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Kisnney Almeida
Keyword(s):  
Artin Groups

AbstractWe classify the Bieri–Neumann–Strebel invariant

Quantum Homomorphisms of Associative Algebras

1997 ◽  
Vol 12 (38) ◽  
pp. 2963-2974
Author(s):  
A. E. F. Djemai
Keyword(s):  
Quantum Group ◽  
Associative Algebra ◽  
Associative Algebras ◽  
Type Formula ◽  
Algebra Of Functions ◽  
Inhomogeneous Quantum

Given an associative algebra A generated by {ek, k=1, 2,…} and with an internal law of type: [Formula: see text], we first show that it is possible to construct a quantum bi-algebra [Formula: see text] with unit and generated by (non-necessarily commutative) elements [Formula: see text] satisfying the relations: [Formula: see text]. This leads one to define a quantum homomorphism[Formula: see text]. We then treat the example of the algebra of functions on a set of N elements and we show, for the case N=2, that the resulting bihyphen;algebra is an inhomogeneous quantum group. We think that this method can be used to construct quantum inhomogeneous groups.

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