An Unexpected Cyclic Symmetry of $$I{\mathfrak u}_n$$

Abstract

AbstractWe find and discuss an unexpected (to us) order n cyclic group of automorphisms of the Lie algebra $$I{\mathfrak u}_n{:}{=}{\mathfrak u}_n < imes {\mathfrak u}_n^*$$ I u n : = u n ⋉ u n ∗ , where $${\mathfrak u}_n$$ u n is the Lie algebra of upper triangular $$n\times n$$ n × n matrices. Our results also extend to $$\mathfrak {gl}_{n+}^\epsilon $$ gl n + ϵ , a “solvable approximation” of $$\mathfrak {gl}_n$$ gl n , as defined within.