Box products in nilpotent normal form theory: The factoring method

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Murdock, James¹ 

[1] Iowa State Univ, Dept Math, Ames, IA 50011 USA

关键词: Normal forms;    Vector fields;    Nilpotent linear part;    Stanley decompositions;    Invariant theory;    Stanley decompositions;   

DOI  :  10.1016/j.jde.2015.09.018

来源: Elsevier

【 摘 要 】

Let N be a nilpotent matrix and consider vector fields (x) over dot = Nx + v(x) in normal form. Then v is equivariant under the flow e(N*t) for the inner product normal form or e(Mt) for the sl(2) normal form. These vector equivariants can be found by finding the scalar invariants for the Jordan blocks in N* or M; taking the box product of these to obtain the invariants for N* or M itself; and then boosting the invariants to equivariants by another box product. These methods, developed by Murdock and Sanders in 2007, are here given a self-contained exposition with new foundations and new algorithms yielding improved (simpler) Stanley decompositions for the invariants and equivariants. Ideas used include transvectants (from classical invariant theory), Stanley decompositions (from commutative algebra), and integer cones (from integer programming). This approach can be extended to covariants of sl(2)(k) for k > 1, known as SLOCC in quantum computing. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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