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On the global and <f>∇</f>-filtration dimensions of quasi-hereditary algebras
- Source :
-
Journal of Pure & Applied Algebra . Nov2004, Vol. 194 Issue 1/2, p95-111. 17p. - Publication Year :
- 2004
-
Abstract
- In this paper, we consider how the <f>∇</f>-, <f>Δ</f>- and global dimensions of a quasi-hereditary algebra are interrelated. We first consider quasi-hereditary algebras with simple preserving duality and such that if <f>μ<λ</f> then <f>∇.f.d.(L(μ))<∇.f.d.(L(λ))</f>, where <f>μ, λ</f> are in the poset and <f>L(μ), L(λ)</f> are the corresponding simples. We show that in this case the global dimension of the algebra is twice its <f>∇</f>-filtration dimension. We then consider more general quasi-hereditary algebras and look at how these dimensions are affected by the Ringel dual and by two forms of truncation. We restrict again to quasi-hereditary algebras with simple preserving duality and consider various orders on the poset compatible with quasi-hereditary structure and the <f>∇</f>-, <f>Δ</f>- and injective dimensions of the simple and the costandard modules. [Copyright &y& Elsevier]
- Subjects :
- *ALGEBRA
*MATHEMATICS
*ARITHMETIC
*EQUATIONS
Subjects
Details
- Language :
- English
- ISSN :
- 00224049
- Volume :
- 194
- Issue :
- 1/2
- Database :
- Academic Search Index
- Journal :
- Journal of Pure & Applied Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 14187923
- Full Text :
- https://doi.org/10.1016/j.jpaa.2004.04.005