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Ringel duality and Auslander–Dlab–Ringel algebras

(2018) JOURNAL OF PURE AND APPLIED ALGEBRA. 222(12). p.3831-3848
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Organization
Abstract
We introduce a new class of quasi-hereditary algebras, containing in particular the Auslander-Dlab-Ringel (ADR) algebras. We show that this new class of algebras is preserved under Ringel duality, which determines in particular explicitly the Ringel dual of any ADR algebra. As a special case of our theory, it follows that, under very restrictive conditions, an ADR algebra is Ringel dual to another one. The latter provides an alternative proof for a recent result of Conde and Erdmann, and places it in a more general setting.
Keywords
Algebra and Number Theory

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Citation

Please use this url to cite or link to this publication:

Chicago
Coulembier, Kevin. 2018. “Ringel Duality and Auslander–Dlab–Ringel Algebras.” Journal of Pure and Applied Algebra 222 (12): 3831–3848.
APA
Coulembier, K. (2018). Ringel duality and Auslander–Dlab–Ringel algebras. JOURNAL OF PURE AND APPLIED ALGEBRA, 222(12), 3831–3848.
Vancouver
1.
Coulembier K. Ringel duality and Auslander–Dlab–Ringel algebras. JOURNAL OF PURE AND APPLIED ALGEBRA. PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS: Elsevier; 2018;222(12):3831–48.
MLA
Coulembier, Kevin. “Ringel Duality and Auslander–Dlab–Ringel Algebras.” JOURNAL OF PURE AND APPLIED ALGEBRA 222.12 (2018): 3831–3848. Print.
@article{8604616,
  abstract     = {We introduce a new class of quasi-hereditary algebras, containing in particular the Auslander-Dlab-Ringel (ADR) algebras. We show that this new class of algebras is preserved under Ringel duality, which determines in particular explicitly the Ringel dual of any ADR algebra. As a special case of our theory, it follows that, under very restrictive conditions, an ADR algebra is Ringel dual to another one. The latter provides an alternative proof for a recent result of Conde and Erdmann, and places it in a more general setting.},
  author       = {Coulembier, Kevin},
  issn         = {0022-4049},
  journal      = {JOURNAL OF PURE AND APPLIED ALGEBRA},
  keywords     = {Algebra and Number Theory},
  language     = {eng},
  number       = {12},
  pages        = {3831--3848},
  publisher    = {Elsevier},
  title        = {Ringel duality and Auslander–Dlab–Ringel algebras},
  url          = {http://dx.doi.org/10.1016/j.jpaa.2018.02.009},
  volume       = {222},
  year         = {2018},
}

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