کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6426190 | 1346077 | 2014 | 16 صفحه PDF | دانلود رایگان |
For any involution Ï of a semisimple Lie algebra g, one constructs a non-reductive Lie algebra k, which is called a Z2-contraction of g. In this paper, we attack the problem of describing maximal commutative subalgebras of the Poisson algebra S(k). This is closely related to the study of the coadjoint representation of k and the set, kregâ, of the regular elements of kâ. By our previous results, in the context of Z2-contractions, the argument shift method provides maximal commutative subalgebras of S(k) whenever codim(kââkregâ)⩾3.Our main result here is that codim(kââkregâ)⩾3 if and only if the Satake diagram of Ï has no trivial nodes. (A node is trivial, if it is white, has no arrows attached, and all adjacent nodes are also white.) The list of suitable involutions is provided. We also describe certain maximal commutative subalgebras of S(k) if the (â1)-eigenspace of Ï in g contains regular elements.
Journal: Bulletin des Sciences Mathématiques - Volume 138, Issue 6, September 2014, Pages 705-720