The quadratic sum problem for symplectic pairs

被引：0
|
作者：
Pazzis, Clement de Seguins [1 ]
机构：
[1] Univ Versailles St Quentin En Yvelines, Lab Math Versailles, 45 Ave Etats Unis, F-78035 Versailles, France
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2024年 / 683卷
关键词：
Symplectic forms; Invariant factors; Quadratic elements; Decomposition; MATRICES; PRODUCTS;
D O I：
10.1016/j.laa.2023.12.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let (b, u) be a pair consisting of a symplectic form b on a finite-dimensional vector space V over a field F, and of a b -alternating endomorphism u of V (i.e. b(x, u(x)) = 0 for all x in V ). Let p and q be arbitrary polynomials of degree 2 with coefficients in F. We characterize, in terms of the invariant factors of u, the condition that u splits into u1 + u2 for some pair (u1, u2) of b-alternating endomorphisms such that p(u1) = q(u2) = 0. (c) 2023 Elsevier Inc. All rights reserved.
引用
收藏
页码：151 / 179
页数：29
相关论文
共 50 条
  • [21] Stability theorems for symplectic and contact pairs
    Bande, G
    Ghiggini, P
    Kotschick, D
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2004, 2004 (68) : 3673 - 3688
  • [22] Local rigidity and nonrigidity of symplectic pairs
    Calvino-Louzao, E.
    Garcia-Rio, E.
    Vazquez-Abal, M. E.
    Vazquez-Lorenzo, R.
    ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2012, 41 (02) : 241 - 252
  • [23] Local rigidity and nonrigidity of symplectic pairs
    E. Calviño-Louzao
    E. García-Río
    M. E. Vázquez-Abal
    R. Vázquez-Lorenzo
    Annals of Global Analysis and Geometry, 2012, 41 : 241 - 252
  • [24] Symplectic Pairs and Intrinsically Harmonic Forms
    Bande, Gianluca
    MATHEMATICS, 2023, 11 (13)
  • [25] Almost complex structures for symplectic pairs
    Her, Hai-Long
    TOPOLOGY AND ITS APPLICATIONS, 2018, 235 : 35 - 42
  • [26] On the geometry and quantization of symplectic Howe pairs
    Balleier, Carsten
    Wurzbacher, Tilmann
    MATHEMATISCHE ZEITSCHRIFT, 2012, 271 (1-2) : 577 - 591
  • [27] Moser’s Quadratic, Symplectic Map
    Arnd Bäcker
    James D. Meiss
    Regular and Chaotic Dynamics, 2018, 23 : 654 - 664
  • [28] QUADRATIC BRACKETS FROM SYMPLECTIC FORMS
    ALEKSEEV, AY
    TODOROV, IT
    NUCLEAR PHYSICS B, 1994, 421 (02) : 413 - 428
  • [29] QUADRATIC CONSERVATIVES OF LINEAR SYMPLECTIC SYSTEM
    MAEDA, S
    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1988, 64 (02) : 45 - 48
  • [30] On the geometry and quantization of symplectic Howe pairs
    Carsten Balleier
    Tilmann Wurzbacher
    Mathematische Zeitschrift, 2012, 271 : 577 - 591
12345