منابع مشابه
Products of commuting nilpotent operators
Matrices that are products of two (or more) commuting square-zero matrices and matrices that are products of two commuting nilpotent matrices are characterized. Also given are characterizations of operators on an infinite dimensional Hilbert space that are products of two (or more) commuting square-zero operators, as well as operators on an infinite-dimensional vector space that are products of...
متن کاملOn Pairs of Commuting Nilpotent Matrices
Let B be a nilpotent matrix and suppose that its Jordan canonical form is determined by a partition λ. Then it is known that its nilpotent commutator NB is an irreducible variety and that there is a unique partition μ such that the intersection of the orbit of nilpotent matrices corresponding to μ with NB is dense in NB. We prove that map D given by D(λ) = μ is an idempotent map. This answers a...
متن کاملOn the Centralizer of the Sum of Commuting Nilpotent Elements
Let X and Y be commuting nilpotent K-endomorphisms of a vector space V , where K is a field of characteristic p ≥ 0. If F = K(t) is the field of rational functions on the projective line P1/K , consider the K(t)-endomorphism A = X+ tY of V . If p = 0, or if A = 0, we show here that X and Y are tangent to the unipotent radical of the centralizer of A in GL(V ). For all geometric points (a : b) o...
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Let V be a vector space of dimension n over a fieldK of characteristic equal to 0 or ≥ n/2. Let g = gln(V ) and n be the nilcone of g, i.e., the cone of nilpotent matrices of g. We write elements of V and V ∗ as column and row vectors, respectively. In this paper we study the variety N := {(X,Y, i, j) ∈ n× n × V × V ∗ | [X,Y ] + ij = 0} and prove that it has n irreducible components: 2 of dimen...
متن کاملFields with several Commuting Derivations
The existentially closed models of the theory of fields (of arbitrary characteristic) with a given finite number of commuting derivations can be characterized geometrically, in several ways. In each case, the existentially closed models are those models that contain points of certain differential varieties, which are determined by certain ordinary varieties. How can we tell whether a given syst...
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ژورنال
عنوان ژورنال: Nuclear Physics B - Proceedings Supplements
سال: 1994
ISSN: 0920-5632
DOI: 10.1016/0920-5632(94)90435-9