Quivers with relations arising from Koszul algebras of g-invariants

JOURNAL OF ALGEBRA

卷:322

Article

Greenstein, Jacob

关键词: Koszul algebras;    Quivers;    Path algebras;    Current algebras;    Invariants;   

DOI  :  10.1016/j.jalgebra.2009.09.032

来源: Elsevier

【 摘 要 】

Let g be a complex simple Lie algebra and let psi be an extremal set of positive roots. After Chad and Greenstein (2009) [9], one associates with psi an infinite dimensional Koszul algebra S(psi)(g) which is a graded subalgebra of the locally finite part of ((End V)(0p) circle times S(g))(g), where V is the direct sum of all simple finite dimensional g-modules. We describe the structure of the algebra S(psi)(g) explicity in terms of an infinite quiver with relations for g of types A and C. We also describe several infinite families of quivers and finite dimensional associative algebras arising from this construction. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free