An Unexpected Cyclic Symmetry of Iun

Roland van der Veen; Dror Bar-Natan

doi:10.1007/s12188-023-00266-w

An Unexpected Cyclic Symmetry of Iu_n

Roland van der Veen^*
, Dror Bar-Natan^*

^*Corresponding author for this work

Dynamical Systems, Geometry and Mathematical Physics

Research output: Contribution to journal › Article › Academic › peer-review

1 Citation (Scopus)

78 Downloads (Pure)

Abstract

We find and discuss an unexpected (to us) order n cyclic group of automorphisms of the Lie algebra Iun:=un⋉un∗, where u_n is the Lie algebra of upper triangular n× n matrices. Our results also extend to gln+ϵ, a “solvable approximation” of gl_n, as defined within.

Original language	English
Pages (from-to)	71-76
Number of pages	6
Journal	Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume	93
Issue number	1
DOIs	https://doi.org/10.1007/s12188-023-00266-w
Publication status	Published - Apr-2023

Keywords

Lie algebra automorphism
Lie algebras
Lie bialgebras
Solvable approximation
Triangular matrices

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abstract = "We find and discuss an unexpected (to us) order n cyclic group of automorphisms of the Lie algebra Iun:=un⋉un∗, where un is the Lie algebra of upper triangular n× n matrices. Our results also extend to gln+ϵ, a “solvable approximation” of gln, as defined within.",

keywords = "Lie algebra automorphism, Lie algebras, Lie bialgebras, Solvable approximation, Triangular matrices",

author = "Veen, \{Roland van der\} and Dror Bar-Natan",

note = "Funding Information: This work was partially supported by grant RGPIN-2018-04350 of the Natural Sciences and Engineering Research Council of Canada. It is available in electronic form, along with source files and a verification Mathematica notebook at http://drorbn.net/UnexpectedCyclic and at arXiv:2002.00697 . Publisher Copyright: {\textcopyright} 2023, The Author(s).",

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KW - Lie algebra automorphism

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KW - Lie bialgebras

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KW - Triangular matrices

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