کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9493322 | 1334235 | 2005 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Déformation par quantification et rigidité des algèbres enveloppantes
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We call a finite-dimensional complex Lie algebra g strongly rigid if its universal enveloping algebra Ug is rigid as an associative algebra, i.e., every formal associative deformation is equivalent to the trivial deformation. In quantum group theory this phenomenon is well known to be the case for all complex semisimple Lie algebras. We show that a strongly rigid Lie algebra, over a field of characteristic 0, has to be rigid as Lie algebra, and that in addition its second scalar cohomology group has to vanish (which excludes nilpotent Lie algebras of dimension greater or equal than two). Moreover, using Kontsevitch's theory of deformation quantization we show that every polynomial deformation of the linear Poisson structure on gâ which induces a nonzero cohomology class of a complex Lie algebra g leads to a nontrivial deformation of Ug. Hence every Poisson structure on a vector space which is zero at some point and whose linear part is a strongly rigid Lie algebra is therefore formally linearizable in the sense of A. Weinstein. Finally we provide examples of rigid Lie algebras which are not strongly rigid, and give a classification of all strongly rigid Lie algebras up to dimension 6.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 285, Issue 2, 15 March 2005, Pages 623-648
Journal: Journal of Algebra - Volume 285, Issue 2, 15 March 2005, Pages 623-648
نویسندگان
M. Bordemann, A. Makhlouf, T. Petit,