Moduli space of bi-invariant metrics (Q6564826)

The author's summary: In this work, we focus on describing the space of bi-invariant metrics in a Lie group up to isometry, i.e, metrics invariant under both left and right translations. We show that \(\mathfrak{B}\mathfrak{J}\), the moduli space of bi-invariant metrics, is an orbifold. Moreover, we give an explicit description of this orbifold, and of \(\mathfrak{E}\mathfrak{B}\mathfrak{T}\), the space of bi-invariant metrics equivalent under isometries and scalar multiplies.