| Full text | |
| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] Ukrainian Acad Sci, Inst Math, Kiev - Ukraine
[2] Univ Sao Paulo, Dept Math, BR-05508 Sao Paulo - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Linear Algebra and its Applications; v. 437, n. 2, p. 581-588, JUL 15 2012. |
| Web of Science Citations: | 6 |
| Abstract | |
A subspace representation of a poset S = [s(1), ..., S-t] is given by a system (V; V-1, ..., V-t) consisting of a vector space V and its sub-spaces V-i such that V-i subset of V-j if s(i) (sic) S-j. For each real-valued vector chi = (chi(1), ..., chi(t)) with positive components, we define a unitary chi-representation of S as a system (U: U-1, ..., U-t) that consists of a unitary space U and its subspaces U-i such that U-i subset of U-j if S-i (sic) S-j and satisfies chi 1 P-1 + ... + chi P-t(t) = 1, in which P-i is the orthogonal projection onto U-i. We prove that S has a finite number of unitarily nonequivalent indecomposable chi-representations for each weight chi if and only if S has a finite number of nonequivalent indecomposable subspace representations; that is, if and only if S contains any of Kleiner's critical posets. (c) 2012 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 10/15781-0 - Stable vector bundles over projective plane and representations of posets in the category of unitary spaces |
| Grantee: | Kostiantyn Iusenko |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |