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Stratifications of algebras with two simple modules
-
Qunhua Liu
and
Dong Yang
Published/Copyright:
August 19, 2014
Abstract
Let A be a finite-dimensional algebra with two simple modules. It is shown that if the derived category of A admits a stratification with simple factors being the base field k, then A is derived equivalent to a quasi-hereditary algebra. As a consequence, if further k is algebraically closed and A has finite global dimension, then A is either derived simple or derived equivalent to a quasi-hereditary algebra.
MSC: Recollement; stratification; quasi-hereditary algebra; derived simple algebra; Hochschild cohomology
Funding source: Jiangsu Province
Award Identifier / Grant number: BK20130899
Funding source: Natural Science Foundation of China
Award Identifier / Grant number: 11301272
The authors thank a referee for helpful suggestions.
Received: 2013-11-1
Revised: 2014-6-13
Published Online: 2014-8-19
Published in Print: 2016-1-1
© 2016 by De Gruyter
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Articles in the same Issue
- Frontmatter
- On Barnes beta distributions, Selberg integral and Riemann xi
- Multi-parameter Triebel–Lizorkin spaces associated with the composition of two singular integrals and their atomic decomposition
- Littlewood–Paley functions on homogeneous groups
- Boundedness of singular integrals associated to surfaces of revolution on Triebel–Lizorkin spaces
- The cohomology of the sporadic group J2 over 𝔽3
- Categorical representations of the modular group
- On the Koszul map of Lie algebras
- A twisted Bass–Heller–Swan decomposition for the algebraic K-theory of additive categories
- Stratifications of algebras with two simple modules
- Pro-Lie groups approximable by discrete subgroups
- Half the sum of positive roots, the Coxeter element, and a theorem of Kostant
