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Tilting Modules in Truncated Categories
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Tilting Modules in Truncated Categories
Інший ID:
2010 Mathematics Subject Classification: 17B70; 17B65; 17B10; 17B55
DOI:10.3842/SIGMA.2014.030
DOI:10.3842/SIGMA.2014.030
Посилання:
Tilting Modules in Truncated Categories / M. Bennett, A. Bianchi // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 25 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on New Directions in Lie Theory. The full collection is
available at http://www.emis.de/journals/SIGMA/LieTheory2014.html.
The authors are grateful for the stimulating discussions with Professor Adriano Moura as well as
the hospitality of the Institute of Mathematics of the State University of Campinas where most
of this work was completed. We thank the anonymous referees for their significant contributions
towards improving the exposition of this paper. This work was partially supported by FAPESP
grants 2012/06923-0 (M. Bennett) and 2011/22322-4 (A. Bianchi).
Дата:
2014
Переглядів:
477
Завантажень:
245
Анотація:
We begin the study of a tilting theory in certain truncated categories of modules G(Γ) for the current Lie algebra associated to a finite-dimensional complex simple Lie algebra, where Γ=P+×J, J is an interval in Z, and P+ is the set of dominant integral weights of the simple Lie algebra. We use this to put a tilting theory on the category G(Γ′) where Γ′=P′×J, where P′⊆P+ is saturated. Under certain natural conditions on Γ′, we note that G(Γ′) admits full tilting modules.
