CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
  location:  Publicationsjournals
Publications        
Search results

Search: MSC category 15A21 ( Canonical forms, reductions, classification )

  Expand all        Collapse all Results 1 - 2 of 2

1. CMB Online first

Leandro, Cagliero; Szechtman, Fernando
Jordan-Chevalley decomposition in Lie algebras
We prove that if $\mathfrak{s}$ is a solvable Lie algebra of matrices over a field of characteristic 0, and $A\in\mathfrak{s}$, then the semisimple and nilpotent summands of the Jordan-Chevalley decomposition of $A$ belong to $\mathfrak{s}$ if and only if there exist $S,N\in\mathfrak{s}$, $S$ is semisimple, $N$ is nilpotent (not necessarily $[S,N]=0$) such that $A=S+N$.

Keywords:solvable Lie algebra, Jordan-Chevalley decomposition, representation
Categories:17-08, 17B05, 20C40, 15A21

2. CMB 2016 (vol 59 pp. 311)

Ilten, Nathan; Teitler, Zach
Product Ranks of the $3\times 3$ Determinant and Permanent
We show that the product rank of the $3 \times 3$ determinant $\det_3$ is $5$, and the product rank of the $3 \times 3$ permanent $\operatorname{perm}_3$ is $4$. As a corollary, we obtain that the tensor rank of $\det_3$ is $5$ and the tensor rank of $\operatorname{perm}_3$ is $4$. We show moreover that the border product rank of $\operatorname{perm}_n$ is larger than $n$ for any $n\geq 3$.

Keywords:product rank, tensor rank, determinant, permanent, Fano schemes
Categories:15A21, 15A69, 14M12, 14N15

© Canadian Mathematical Society, 2019 : https://cms.math.ca/