کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4599834 1336825 2013 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The poset of the nilpotent commutator of a nilpotent matrix
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
The poset of the nilpotent commutator of a nilpotent matrix
چکیده انگلیسی

Let B   be an n×nn×n nilpotent matrix with entries in an infinite field kk. The nilpotent commutator NBNB of B is known to be an irreducible algebraic variety. Assume that B is in Jordan canonical form with the associated Jordan block partition P   and let Q(P)Q(P) be the Jordan partition of a generic element of NBNB. P. Oblak associated to a given partition P   another partition resulting from a recursive process. She conjectured that this partition is the same as Q(P)Q(P). R. Basili, A. Iarrobino and the author later generalized the process introduced by Oblak. The main result of this paper states that all such processes give rise to the same partition – a partition that is defined in terms of the lengths of unions of special symmetric chains in a poset associated to NBNB. This poset was defined by P. Oblak as the digraph determined by the non-zero entries of a generic matrix in a maximal nilpotent subalgebra of NBNB.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 439, Issue 12, 15 December 2013, Pages 3763–3776
نویسندگان
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