Extending the nonrelativistic string AdS coset

Abstract

Inspired by Lie algebra expansion, we consider an extension of the algebra introduced in A. Fontanella and S. J. van Tongeren [Coset space actions for nonrelativistic strings, J. High Energy Phys. 06 (2022) 80.] for the nonrelativistic string coset action in ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$. We show that the extended algebra admits a nondegenerate inner product which is adjoint invariant under the full extended algebra. Furthermore, we provide a finite-dimensional representation of the extended algebra.