Tensor hierarchy algebras occurred in mathematical physics, especially in extended geometry and gauged supergravity. Physicists have noticed tensor hierarchies present a very deep and intriguing relationship with Leibniz algebras and what are called their infinity enhancements. Work of Sylvain Lavau has shown how any Leibniz algebra gives rise to a differential graded Lie algebra and an associated tensor hierarchy with a corresponding infinity-enhanced Leibniz algebra. Moreover, by a theorem of Getzler, this differential graded Lie algebra canonically induces an L∞-algebra structure (not the obvious one). I will report on work in progress with Lavau to further elucidate and make more accessible to mathematicians these new objects and his procedures.

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