The gauge structure and pseudo-action of extended geometry with ancillary transformations are encoded by a tensor hierarchy algebra S(g+), yielding a partial L-infinity description for finite-dimensional structure groups.
Higher Gauge Structures in Double and Exceptional Field Theory
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abstract
We review the higher gauge symmetries in double and exceptional field theory from the viewpoint of an embedding tensor construction. This is based on a (typically infinite-dimensional) Lie algebra $\frak{g}$ and a choice of representation $R$. The embedding tensor is a map from the representation space $R$ into $\frak{g}$ satisfying a compatibility condition (`quadratic constraint'). The Lie algebra structure on $\frak{g}$ is transported to a Leibniz--Loday algebra on $R$, which in turn gives rise to an $L_{\infty}$-structure. We review how the gauge structures of double and exceptional field theory fit into this framework.
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Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
The gauge structure and pseudo-action of extended geometry with ancillary transformations are encoded by a tensor hierarchy algebra S(g+), yielding a partial L-infinity description for finite-dimensional structure groups.