scholarly journals Exchange relation planar algebras of small rank

2016 ◽  
Vol 368 (12) ◽  
pp. 8303-8348 ◽  
Author(s):  
Zhengwei Liu
Keyword(s):  
Planar Algebras ◽  
Small Rank ◽  
Exchange Relation

scholarly journals NON-SYMPLECTIC INVOLUTIONS ON MANIFOLDS OF -TYPE

2020 ◽  
pp. 1-25
Author(s):  
CHIARA CAMERE ◽  
ALBERTO CATTANEO ◽  
ANDREA CATTANEO
Keyword(s):  
Moduli Spaces ◽  
Quadratic Forms ◽  
Symplectic Manifolds ◽  
Hilbert Schemes ◽  
Small Rank ◽  
Twisted Sheaves ◽  
Formula Type

We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a $K3$ surface and admitting a non-symplectic involution. We classify the possible discriminant quadratic forms of the invariant and coinvariant lattice for the action of the involution on cohomology and explicitly describe the lattices in the cases where the invariant lattice has small rank. We also give a modular description of all $d$ -dimensional families of manifolds of $K3^{[n]}$ -type with a non-symplectic involution for $d\geqslant 19$ and $n\leqslant 5$ and provide examples arising as moduli spaces of twisted sheaves on a $K3$ surface.

Singly generated planar algebras of small dimension

2000 ◽  
Vol 101 (1) ◽  
pp. 41-75 ◽  
Author(s):  
Vaughan Jones ◽  
Dietmar Bisch
Keyword(s):  
Small Dimension ◽  
Planar Algebras

Automorphisms with centralizers of small rank

2010 ◽  
pp. 564-585 ◽  
Author(s):  
Evgeny Khukhro ◽  
Victor Mazurov
Keyword(s):  
Small Rank

scholarly journals Constructions of Chiral Polytopes of Small Rank

2011 ◽  
Vol 63 (6) ◽  
pp. 1254-1283 ◽  
Author(s):  
Antonio Breda D’Azevedo ◽  
Gareth A. Jones ◽  
Egon Schulte
Keyword(s):  
Automorphism Group ◽  
Small Rank ◽  
Abstract Polytope ◽  
Chiral Polytopes ◽  
General Method

AbstractAn abstract polytope of rank n is said to be chiral if its automorphism group has precisely two orbits on the flags, such that adjacent flags belong to distinct orbits. This paper describes a general method for deriving new finite chiral polytopes from old finite chiral polytopes of the same rank. In particular, the technique is used to construct many new examples in ranks 3, 4, and 5.

scholarly journals Free Product C* -algebras Associated with Graphs, Free Differentials, and Laws of Loops

2017 ◽  
Vol 69 (3) ◽  
pp. 548-578 ◽  
Author(s):  
Michael Hartglass
Keyword(s):  
Differential Calculus ◽  
Von Neumann Algebras ◽  
Sufficient Conditions ◽  
Weighted Graph ◽  
Positive Cone ◽  
Von Neumann ◽  
Planar Algebras ◽  
C Algebra ◽  
C Algebras ◽  
Necessary And Sufficient

AbstractWe study a canonical C* -algebra, 𝒮(Г,μ), that arises from a weighted graph (Г,μ), speci fic cases of which were previously studied in the context of planar algebras. We discuss necessary and sufficient conditions of the weighting that ensure simplicity and uniqueness of trace of 𝒮(Г,μ), and study the structure of its positive cone. We then study the *-algebra,𝒜, generated by the generators of 𝒮(Г,μ), and use a free differential calculus and techniques of Charlesworth and Shlyakhtenko as well as Mai, Speicher, and Weber to show that certain “loop” elements have no atoms in their spectral measure. After modifying techniques of Shlyakhtenko and Skoufranis to show that self adjoint elements x ∊ Mn(𝒜) have algebraic Cauchy transform, we explore some applications to eigenvalues of polynomials inWishart matrices and to diagrammatic elements in von Neumann algebras initially considered by Guionnet, Jones, and Shlyakhtenko.

scholarly journals Some remarks on regular foliations with numerically trivial canonical class

2017 ◽  
Vol Volume 1 ◽  
Author(s):  
Stéphane Druel
Keyword(s):  
Small Rank ◽  
Codimension Two ◽  
Canonical Class ◽  
Special Cases ◽  
Algebraicity Criterion ◽  
Projective Manifolds ◽  
Complex Projective ◽  
Algebraic Foliations

In this article, we first describe codimension two regular foliations with numerically trivial canonical class on complex projective manifolds whose canonical class is not numerically effective. Building on a recent algebraicity criterion for leaves of algebraic foliations, we then address regular foliations of small rank with numerically trivial canonical class on complex projective manifolds whose canonical class is pseudo-effective. Finally, we confirm the generalized Bondal conjecture formulated by Beauville in some special cases. Comment: 20 pages

Approximation of Toeplitz matrices by sums of circulants and small-rank matrices

2006 ◽  
Vol 73 (1) ◽  
pp. 100-101 ◽  
Author(s):  
N. L. Zamarashkin ◽  
I. V. Oseledets ◽  
E. E. Tyrtyshnikov
Keyword(s):  
Toeplitz Matrices ◽  
Small Rank
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