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arXiv · 1403.4623

Idempotents in nonassociative algebras and eigenvectors of quadratic operators

Yuri Lyubich·Alexander Tsukerman
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Abstract

Let $F$ be a field, char$(F)\neq 2$. Then every finite-dimensional $F$-algebra has either an idempotent or an absolute nilpotent if and only if over $F$ every polynomial of odd degree has a root in $F$. This is also necessary and sufficient for existence of eigenvectors for all quadratic operators in finite-dimensional spaces over $F$.

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Yuri Lyubich, Alexander Tsukerman. 2014-03-18. Idempotents in nonassociative algebras and eigenvectors of quadratic operators. https://arxiv.org/abs/1403.4623

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