Kac–Moody algebras of affine type

2005 ◽  
pp. 386-415
Keyword(s):  
Affine Type

Stability conditions and braid group actions on affine An quivers

2021 ◽  
pp. 2250174
Author(s):  
Chien-Hsun Wang
Keyword(s):  
Moduli Space ◽  
Braid Group ◽  
Group Actions ◽  
Stability Conditions ◽  
Quadratic Differentials ◽  
Spherical Subgroup ◽  
Type Formula ◽  
Affine Type

We study stability conditions on the Calabi–Yau-[Formula: see text] categories associated to an affine type [Formula: see text] quiver which can be constructed from certain meromorphic quadratic differentials with zeroes of order [Formula: see text]. We follow Ikeda’s work to show that this moduli space of quadratic differentials is isomorphic to the space of stability conditions quotient by the spherical subgroup of the autoequivalence group. We show that the spherical subgroup is isomorphic to the braid group of affine type [Formula: see text] based on the Khovanov–Seidel–Thomas method.

scholarly journals Combinatorial Interpretations for Rank-Two Cluster Algebras of Affine Type

10.37236/933 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Gregg Musiker ◽  
James Propp
Keyword(s):  
Lie Algebras ◽  
Cluster Algebras ◽  
Laurent Polynomials ◽  
Finite Dimensional ◽  
Combinatorial Interpretations ◽  
Rank 2 ◽  
The Individual ◽  
Affine Type ◽  
Positive Integers ◽  
Two Parameter

Fomin and Zelevinsky show that a certain two-parameter family of rational recurrence relations, here called the $(b,c)$ family, possesses the Laurentness property: for all $b,c$, each term of the $(b,c)$ sequence can be expressed as a Laurent polynomial in the two initial terms. In the case where the positive integers $b,c$ satisfy $bc < 4$, the recurrence is related to the root systems of finite-dimensional rank $2$ Lie algebras; when $bc>4$, the recurrence is related to Kac-Moody rank $2$ Lie algebras of general type. Here we investigate the borderline cases $bc=4$, corresponding to Kac-Moody Lie algebras of affine type. In these cases, we show that the Laurent polynomials arising from the recurence can be viewed as generating functions that enumerate the perfect matchings of certain graphs. By providing combinatorial interpretations of the individual coefficients of these Laurent polynomials, we establish their positivity.

2- $$(v,k,1)$$ ( v , k , 1 ) Designs with a point-primitive rank 3 automorphism group of affine type

2014 ◽  
Vol 76 (2) ◽  
pp. 135-171 ◽  
Author(s):  
Mauro Biliotti ◽  
Alessandro Montinaro ◽  
Eliana Francot
Keyword(s):  
Automorphism Group ◽  
Affine Type

Gröbner-Shirshov Basis of Twisted Generic Composition Algebras of Affine Type

2017 ◽  
Vol 24 (01) ◽  
pp. 109-122
Author(s):  
Gulshadam Yunus ◽  
Abdukadir Obul
Keyword(s):  
Indecomposable Representations ◽  
Generic Composition ◽  
Composition Algebras ◽  
Affine Type

In this paper, by using PBW bases for the twisted generic composition algebras of affine type, we prove that the set of the skew-commutator relations of the iso-classes of indecomposable representations forms a minimal Gröbner-Shirshov basis for the twisted generic composition algebras of affine type.

FRACTAL CHARACTERISTICS OF THE HORIZONTAL MOVEMENT OF WATER IN SOILS

Fractals ◽  
1994 ◽  
Vol 02 (03) ◽  
pp. 465-468 ◽  
Author(s):  
IVAN A. GUERRINI ◽  
D. SWARTZENDRUBER
Keyword(s):  
Brownian Motion ◽  
Soil Water ◽  
Unsaturated Soils ◽  
Water Movement ◽  
Water Saturation ◽  
Horizontal Movement ◽  
Water Diffusivity ◽  
Fractal Characteristics ◽  
Affine Type ◽  
Soil Water Movement

Observed deviations from traditional concepts of soil-water movement are considered in terms of fractals. A connection is made between this movement and a Brownian motion, a random and self-affine type of fractal, to account for the soil-water diffusivity function having auxiliary time dependence for unsaturated soils. The position of a given water content is directly proportional to tn, where t is time, and exponent n for distinctly unsaturated soil is less than the traditional 0.50. As water saturation is approached, n approaches 0.50. Macroscopic fractional Brownian motion is associated with n < 0.50, but shifts to regular Brownian motion for n = 0.50.

On Flag-Transitive Symmetric Designs of Affine Type

2016 ◽  
Vol 25 (2) ◽  
pp. 85-97 ◽  
Author(s):  
Mauro Biliotti ◽  
Alessandro Montinaro
Keyword(s):  
Symmetric Designs ◽  
Affine Type
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