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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the global dimension of quasi--hereditary algebras with triangular decomposition


Author: Steffen König
Journal: Proc. Amer. Math. Soc. 124 (1996), 1993-1999
MSC (1991): Primary 16E10, 18G20; Secondary 16G10, 17B10, 17B35, 18G05, 20G05
MathSciNet review: 1346979
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $A$ be a quasi--hereditary algebra with triangular decomposition ${_C}A_{C^{op}} \simeq C \otimes _S C^{op}$ such that all Verma modules are semisimple over $C^{op}$. Then we show: $gldim(A) = 2 \cdot gldim(C)$. Applying this formula to the more special class of twisted double incidence algebras of finite partially ordered sets, we get a proof of a conjecture of Deng and Xi. Another application is to the so-called dual extensions of algebras.


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Additional Information

Steffen König
Affiliation: Mathematisches Institut B, Universität Stuttgart, Pfaffenwaldring 57, D–70 569 Stuttgart, Federal Republic of Germany
Address at time of publication: Fakultät für Mathematik, Universität Bielefeld, Postfach 10 01 31, D–33 501 Bielefeld, FR Germany
Email: koenigs@mathematik.uni-bielefeld.de

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03549-6
PII: S 0002-9939(96)03549-6
Received by editor(s): March 25, 1994
Received by editor(s) in revised form: July 1, 1994, and February 21, 1995
Communicated by: Ken Goodearl
Article copyright: © Copyright 1996 American Mathematical Society