Lorentzian Algebraic Ricci Solitons on the Heisenberg Group

There exist three nonequivalent left invariant Lorentzian metrics on the Heisenberg group $H_{2n+1}$, or equivalently, three nonequivalent Lorentzian inner products on the Heisenberg Lie algebra $\mathfrak{h}_{2n+1}$, denoted by $μ$, $ν$, and $ϕ$. We show that, in a specific case, $μ$ is an algebrai