Direct Sum Decomposability of Polynomials

Weronika Buczýnska, Jarosław Buczýnski, Zach Teitler

Research output: Contribution to conferencePresentation

Abstract

<p> A form <em> F </em> = <em> F </em> ( <em> x </em> <sub> 1 </sub> ,..., <em> x <sub> n </sub> </em> ) is decomposable as a direct sum if, possibly after a linear change of coordinates, <em> F </em> = <em> F </em> <sub> 1 </sub> ( <em> x </em> <sub> 1 </sub> ,..., <em> x <sub> k </sub> </em> ) + <em> F </em> <sub> 2 </sub> ( <em> x <sub> k+1 </sub> </em> ,..., <em> x <sub> n </sub> </em> ). For example, <em> xy </em> = &frac14; ( <em> x </em> + <em> y </em> ) <sup> 2 </sup> &minus; &frac14; ( <em> x </em> &minus; <em> y </em> ) <sup> 2 </sup> and the 2 &times; 2 determinant <em> ad&minus;bc </em> are direct sums. General forms are indecomposable as direct sums, but this can be hard to show for particular forms. We give an interesting necessary criterion for a form to be a direct sum and use it to answer a question of Sha&filig;ei. We investigate the indecomposable forms satisfying our criterion.</p>
Original languageAmerican English
StatePublished - 1 Aug 2013
EventSIAM (Society for Industrial and Applied Mathematics) Conference on Applied Algebraic Geometry -
Duration: 2 Aug 2013 → …

Conference

ConferenceSIAM (Society for Industrial and Applied Mathematics) Conference on Applied Algebraic Geometry
Period2/08/13 → …

EGS Disciplines

  • Mathematics

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