Finiteness conditions on the Ext-algebra of a cycle algebra

JOURNAL OF ALGEBRA

卷:310

Article

Davis, Gabriel

关键词: Ext-algebra;    finite generation;    Noetherian;    monomial algebra;    cycle algebra;   

DOI  :  10.1016/j.jalgebra.2004.08.022

来源: Elsevier

【 摘 要 】

Let A be a finite-dimensional algebra given by quiver and monomial relations. In [E.L. Green, D. Zacharia, Manuscripta Math. 85 (1994) 11-23] we see that the Ext-algebra of A is finitely generated only if all the Ext-algebras of certain cycle algebras overlying A are finitely generated. Here a cycle algebra Lambda is a finite-dimensional algebra given by quiver and monomial relations where the quiver is an oriented cycle. The main result of this paper gives necessary and sufficient conditions for the Ext-algebra of such a Lambda to be finitely generated; this is achieved by defining a computable invariant of Lambda, the smo-tube. We also give necessary and sufficient conditions for the Ext-algebra of Lambda to be Noetherian. (c) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free