An Unexpected Cyclic Symmetry of $I\mathfrak{u}_n$
Dror Bar-Natan, Roland van der Veen

TL;DR
This paper uncovers an unexpected cyclic symmetry of order n in the automorphism group of a specific Lie algebra constructed from upper triangular matrices, revealing new structural insights.
Contribution
It identifies and analyzes a novel order n cyclic automorphism group of the Lie algebra $Irak{u}_n$, extending the understanding of its symmetry properties.
Findings
Discovery of an order n cyclic automorphism group
Extension of results to a solvable approximation of $gl_n$
Enhanced understanding of Lie algebra symmetries
Abstract
We find and discuss an unexpected (to us) order cyclic group of automorphisms of the Lie algebra , where is the Lie algebra of upper triangular matrices. Our results also extend to , a ``solvable approximation'' of , as defined within.
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Taxonomy
TopicsAdvanced Topics in Algebra · Matrix Theory and Algorithms · Tensor decomposition and applications
