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Classifying torsion classes for algebras with radical square zero via sign decomposition.
- Source :
-
Journal of Algebra . Nov2022, Vol. 610, p167-198. 32p. - Publication Year :
- 2022
-
Abstract
- To study the set of torsion classes of a finite dimensional basic algebra over a field, we use a decomposition, called sign-decomposition, parameterized by elements of { ± 1 } n where n is the number of simple modules. If A is an algebra with radical square zero, then for each ϵ ∈ { ± 1 } n there is a hereditary algebra A ϵ ! with radical square zero and a bijection between the set of torsion classes of A associated to ϵ and the set of faithful torsion classes of A ϵ !. Furthermore, this bijection preserves the property of being functorially finite. From a point of view of tilting theory, it implies that there is a bijection between the set of isomorphism classes of basic two-term silting complexes for A associated to ϵ and the set of isomorphism classes of basic tilting A ϵ ! -modules. As an application, we prove that the number of two-term tilting complexes over Brauer line algebras (respectively, Brauer cycle algebras) having n edges is ( 2 n n ) (respectively, 2 2 n − 1 if n is odd, and ∞ if n is even). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 610
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 158890079
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2022.06.032