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Generalized tilting functors and Ringel–Hall algebras
- Source :
-
Journal of Pure & Applied Algebra . Feb2007, Vol. 208 Issue 2, p445-448. 4p. - Publication Year :
- 2007
-
Abstract
- Abstract: It is known from [M. Auslander, M.I. Platzeck, I. Reiten, Coxeter functors without diagrams, Trans. Amer. Math. Soc. 250 (1979) 1–46] and [C.M. Ringel, PBW-basis of quantum groups, J. Reine Angew. Math. 470 (1996) 51–85] that the Bernstein–Gelfand–Ponomarev reflection functors are special cases of tilting functors and these reflection functors induce isomorphisms between certain subalgebras of Ringel–Hall algebras. In [A. Wufu, Tilting functors and Ringel–Hall algebras, Comm. Algebra 33 (1) (2005) 343–348] the result from [C.M. Ringel, PBW-basis of quantum groups, J. Reine Angew. Math. 470 (1996) 51–85] is generalized to the tilting module case by giving an isomorphism between two Ringel–Hall subalgebras. In [J. Miyashita, Tilting Modules of Finite Projective Dimension, Math. Z. 193 (1986) 113–146] Miyashita generalized the tilting theory by introducing the tilting modules of finite projective dimension. In this paper the result in [A. Wufu, Tilting functors and Ringel–Hall algebras, Comm. Algebra 33 (1) (2005) 343–348] is generalized to the tilting modules of finite projective dimension. [Copyright &y& Elsevier]
- Subjects :
- *MATHEMATICAL analysis
*SET theory
*ALGEBRA
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00224049
- Volume :
- 208
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Pure & Applied Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 23215169
- Full Text :
- https://doi.org/10.1016/j.jpaa.2006.01.008