کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4583917 | 1630456 | 2016 | 53 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the commuting variety of a reductive Lie algebra and other related varieties
ترجمه فارسی عنوان
در تنوع رفت و آمد یک جبر کاهش دهنده دروغ و دیگر انواع مرتبط است
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
The nilpotent cone of a reductive Lie algebra has a desingularization given by the cotangent bundle of the flag variety. Analogously, the nullcone of a Cartesian power of the algebra has a desingularization given by a vector bundle over the flag variety. As for the nullcone, the subvariety of elements whose components are in a same Borel subalgebra, has a desingularization given by a vector bundle over the flag variety. In this note, we study geometrical properties of these varieties. For the study of the commuting variety, the analogous variety to the flag variety is the closure in the Grassmannian of the set of Cartan subalgebras. So some properties of this variety are given. In particular, it is smooth in codimension 1. We introduce the generalized isospectral commuting varieties and give some properties. Furthermore, desingularizations of these varieties are given by fiber bundles over a desingularization of the closure in the Grassmannian of the set of Cartan subalgebras contained in a given Borel subalgebra.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 458, 15 July 2016, Pages 445-497
Journal: Journal of Algebra - Volume 458, 15 July 2016, Pages 445-497
نویسندگان
Jean-Yves Charbonnel, Mouchira Zaiter,