Teleparallelism in the algebraic approach to extended geometry

A bstract Extended geometry is based on an underlying tensor hierarchy algebra. We extend the previously considered L ∞ structure of local symmetries (the diffeomorphisms and their reducibility) to incorporate physical fields, field strengths Bianchi identities, identify these as elements The arise generalised torsion, so naturally occurring complex in algebra $$ \dots \leftarrow \mathrm{torsion}\ \mathrm{BI}'\mathrm{s}\leftarrow \mathrm{torsion}\leftarrow \mathrm{vielbein}\leftarrow \mathrm{diffeomorphism}\ \mathrm{parameters}\leftarrow … ← torsion BI ’ s vielbein diffeomorphism parameters In order obtain equations motion, which are not this complex, (pseudo-)actions, quadratic given for a large class models. This requires considering dual complex. show how invariance under compact subgroup locally defined by metric arises “dual gauge symmetry” associated with certain torsion identity, generalising Lorentz teleparallel formulation gravity. analysis performed finite-dimensional groups, E 5 detailed example. continuation infinite-dimensional cases discussed.