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.

scholarly journals Composition Algebras of Affine Type

1998 ◽  
Vol 206 (2) ◽  
pp. 505-540 ◽  
Author(s):  
Pu Zhang
Keyword(s):  
Composition Algebras ◽  
Affine Type

scholarly journals On the Number of Absolutely Indecomposable Representations of a Quiver

1999 ◽  
Vol 221 (1) ◽  
pp. 29-49 ◽  
Author(s):  
Bert Sevenhant ◽  
Michel Van Den Bergh
Keyword(s):  
Indecomposable Representations

Generic Composition

2002 ◽  
Vol 14 (2) ◽  
pp. 108-122 ◽  
Author(s):  
Yifeng Chen
Keyword(s):  
Generic Composition

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.

Sign in / Sign up

Export Citation Format

Share Document