Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Higher Lie Symmetry in General Relativity

From a physical perspective, higher Lie symmetry, e.g., differential graded Lie algebras (dgla) or L-infinity algebras, are one way to describe symmetry which is only closed on-shell (or up to homotopy). I will describe several examples of dgla symmetry in (classical) general relativity. First, as a warmup, I will explain how symmetry realized as an equivariant action functional can be used to constrain geometry in a neighborhood of infinity in the Palatini—Cartan formulation of gravity. Next, I will illustrate how conserved quantities can be computed using a L-infinity description of Palatini—Cartan gravity. The latter example is based on work with my PhD student Changsun Choi.