scholarly journals Classification of Rank 2 Cluster Varieties

2019 ◽  
Author(s):  
Travis Mandel ◽  
Keyword(s):  
Rank 2 ◽  
Cluster Varieties

Powerfully nilpotent groups of rank 2 or small order

2020 ◽  
Vol 23 (4) ◽  
pp. 641-658
Author(s):  
Gunnar Traustason ◽  
James Williams
Keyword(s):  
Detailed Analysis ◽  
Special Kind ◽  
Nilpotent Groups ◽  
Nilpotency Class ◽  
Central Series ◽  
Rank 2 ◽  
Full Classification

AbstractIn this paper, we continue the study of powerfully nilpotent groups. These are powerful p-groups possessing a central series of a special kind. To each such group, one can attach a powerful nilpotency class that leads naturally to the notion of a powerful coclass and classification in terms of an ancestry tree. In this paper, we will give a full classification of powerfully nilpotent groups of rank 2. The classification will then be used to arrive at a precise formula for the number of powerfully nilpotent groups of rank 2 and order {p^{n}}. We will also give a detailed analysis of the ancestry tree for these groups. The second part of the paper is then devoted to a full classification of powerfully nilpotent groups of order up to {p^{6}}.

scholarly journals Towards the classification of rank-r $$ \mathcal{N} $$ = 2 SCFTs. Part I. Twisted partition function and central charge formulae

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Mario Martone
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Singular Locus ◽  
Companion Paper ◽  
Coulomb Branch ◽  
Energy Limit ◽  
Superconformal Field Theories ◽  
Rank 2 ◽  
Explicit Formulae

Abstract We derive explicit formulae to compute the a and c central charges of four dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $$ \mathcal{N} $$ N = 2 SCFTs which culminate with our $$ \mathcal{N} $$ N = 2 UV-IR simple flavor condition. This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $$ \mathcal{N} $$ N = 2 SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper.This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world.

scholarly journals Classification of skew translation generalized quadrangles, I

2015 ◽  
Vol Vol. 17 no. 1 (Combinatorics) ◽  
Author(s):  
Koen Thas
Keyword(s):  
Generalized Quadrangles ◽  
New Classification ◽  
Open Problems ◽  
International Audience ◽  
Rank 2

Combinatorics International audience We describe new classification results in the theory of generalized quadrangles (= Tits-buildings of rank 2 and type B2), more precisely in the (large) subtheory of skew translation generalized quadrangles (``STGQs''). Some of these involve, and solve, long-standing open problems.

scholarly journals On the classification of $H$-spaces of rank 2

1973 ◽  
Vol 13 (3) ◽  
pp. 611-627 ◽  
Author(s):  
Mamoru Mimura ◽  
Goro Nishida ◽  
Hirosi Toda
Keyword(s):  
Rank 2

scholarly journals A classification of the commutator subgroup of the group of a boundary link

1974 ◽  
Vol 18 (2) ◽  
pp. 216-221
Author(s):  
Bai Ching Chang
Keyword(s):  
Free Product ◽  
Free Group ◽  
Commutator Subgroup ◽  
Free Product With Amalgamation ◽  
Rank 2

In Neuwirth's book “Knot Groups” ([2]), the structure of the commutator subgroup of a knot is studied and characterized. Later Brown and Crowell refined Neuwith's result ([1], and we thus know that ifGis the groups of a knotK, then [G, G] is either free of rank 2g, wheregis the genus ofK, or a nontrivial free product with amalgamation on a free group of rank 2g, and may be written in the form, whereFis free of rank 2g, and the amalgamations are all proper and identical.

Classification of rank 2 GW-rootsystems

1988 ◽  
Vol 23 (1) ◽  
pp. 15-26 ◽  
Author(s):  
Mohammad Q. Hailat
Keyword(s):  
Rank 2

Locally split and locally finite twin buildings of 2-spherical type

1999 ◽  
Vol 1999 (511) ◽  
pp. 119-143 ◽  
Author(s):  
Bernhard Mühlherr
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Algebraic Groups ◽  
Spherical Type ◽  
Locally Finite ◽  
Arbitrary Rank ◽  
Rank 2 ◽  
Twin Buildings

Abstract We prove a fixed point theorem for twin buildings of arbitrary rank. This theorem is then used to construct certain twin buildings whose existence was conjectured in [12]. As a consequence we obtain a classification of twin buildings whose rank 2 residues correspond to split algebraic groups over a field of cardinality at least 4. A similar result follows for twin buildings whose rank 2 residues are finite.

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