An Unexpected Cyclic Symmetry of I\mathfraku_n

2020/02/03 by Dror Bar-Natan, Roland van der Veen, Bar-Natan, Dror +1 · 1 citation
Computer Science · Mathematics · #Advanced Topics in Algebra #Matrix Theory and Algorithms #Tensor decomposition and applications #math.RT #msc:17B45

paper · pdf · doi:10.48550/arxiv.2002.00697

5 pages and a 4 pages Mathematica notebook

arxiv created 2020/02/11 · arxiv updated 2020/02/12

Abstract

We find and discuss an unexpected (to us) order n cyclic group of automorphisms of the Lie algebra I\mathfraku_n := \mathfraku_n\ltimes\mathfraku_n^∗, where \mathfraku_n is the Lie algebra of upper triangular n× n matrices. Our results also extend to gl_n+^ε, a ``solvable approximation'' of gl_n, as defined within.

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