1-quasi-hereditary algebras: Examples and invariant submodules of projectives

2012/01/19 by Daiva Pucinskaite, Daiva Pučinskaitė, Pucinskaite, Daiva
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Rings, Modules, and Algebras #math.RT #msc:16G20

paper · pdf · doi:10.48550/arxiv.1201.4311

14 pages, with figures

arxiv created 2012/01/19 · arxiv updated 2012/01/23

Abstract

In arXiv:1104.4441 it was shown that any 1-quasi-hereditary algebra affords a particular basis which is related to a given partial order on the set of simple modules. We show that the modules generated by these basis-elements are also modules over the endomorphism algebra of some projective indecomposable modules. In case the Ringel-dual of a 1-quasi-hereditary algebra is also 1-quasi-hereditary, we describe all local Delta-good submodules of projective indecomposable modules. We also consider several examples.

Related

• Quasi-hereditary algebras via generator-cogenerators of local self-injective algebras and transfer of Ringel duality
• On strongly quasi-hereditary algebras
• Based quasi-hereditary algebras
• (m,n)-Quasitilted and (m,n)-Almost Hereditary Algebras
• A remark of the number of quasi-hereditary structures