The $\boldsymbol{L_{\infty}}$-structure of noncommutative gravity

Richard J. Szabo

Published 2022-03-29Version 1

We summarise recent perspectives on symmetries of noncommutative field theories based on homotopy algebras. We show how these new viewpoints naturally lead to a new class of noncommutative field theories which possess braided gauge symmetries, and explain in detail their uses in gravity. We review how these considerations lead to a new theory of noncommutative gravity in four dimensions within the Einstein-Cartan-Palatini formalism.