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Finiteness conditions on the Ext-algebra of a cycle algebra
- Source :
-
Journal of Algebra . Apr2007, Vol. 310 Issue 2, p526-568. 43p. - Publication Year :
- 2007
-
Abstract
- Abstract: 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 Λ 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 Λ to be finitely generated; this is achieved by defining a computable invariant of Λ, the smo-tube. We also give necessary and sufficient conditions for the Ext-algebra of Λ to be Noetherian. [Copyright &y& Elsevier]
- Subjects :
- *ALGEBRA
*MATHEMATICS
*INVARIANTS (Mathematics)
*NOETHERIAN rings
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 310
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 24298311
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2004.08.022