The problems of classifying pairs of forms and local algebras with zero cube radical are wild

Genrich Belitskii; Vitalij M. Bondarenko; Ruvim Lipyanski; Vladimir V. Plachotnik; Vladimir V. Sergeichuk

doi:10.1016/j.laa.2004.12.016

The problems of classifying pairs of forms and local algebras with zero cube radical are wild

Genrich Belitskii, Vitalij M. Bondarenko, Ruvim Lipyanski, Vladimir V. Plachotnik, Vladimir V. Sergeichuk

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We prove that over an algebraically closed field of characteristic not two the problems of classifying pairs of sesquilinear forms in which the second is Hermitian, pairs of bilinear forms in which the second is symmetric (skew-symmetric), and local algebras with zero cube radical and square radical of dimension 2 are hopeless since each of them reduces to the problem of classifying pairs of n-by-n matrices up to simultaneous similarity.

Original language	English
Pages (from-to)	135-142
Number of pages	8
Journal	Linear Algebra and Its Applications
Volume	402
Issue number	1-3
DOIs	https://doi.org/10.1016/j.laa.2004.12.016
State	Published - 1 Jun 2005

Keywords

Local algebras
Pairs of bilinear forms
Wild problems

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2004.12.016

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abstract = "We prove that over an algebraically closed field of characteristic not two the problems of classifying pairs of sesquilinear forms in which the second is Hermitian, pairs of bilinear forms in which the second is symmetric (skew-symmetric), and local algebras with zero cube radical and square radical of dimension 2 are hopeless since each of them reduces to the problem of classifying pairs of n-by-n matrices up to simultaneous similarity.",

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AU - Lipyanski, Ruvim

AU - Plachotnik, Vladimir V.

AU - Sergeichuk, Vladimir V.

PY - 2005/6/1

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AB - We prove that over an algebraically closed field of characteristic not two the problems of classifying pairs of sesquilinear forms in which the second is Hermitian, pairs of bilinear forms in which the second is symmetric (skew-symmetric), and local algebras with zero cube radical and square radical of dimension 2 are hopeless since each of them reduces to the problem of classifying pairs of n-by-n matrices up to simultaneous similarity.

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The problems of classifying pairs of forms and local algebras with zero cube radical are wild

Abstract

Keywords

ASJC Scopus subject areas

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