# Symmetry charges in reduced phase space and their algebra (Hongwei Tan, Florida Atlantic University) FAU^2 Talk

The investigation of boundary charges in asymptotically flat spacetime drew a lot of attention in recent years, which has provided us valuable insight and significantly enhanced our general understanding of gravity. However, most of previous studies along this line are based on the traditional general relativity, which is a pure constraint theory in the bulk. The boundary charges based on the reduced phase are less known to the community. In this talk, I will discuss our recent progress in the symmetry charges (including the bulk parts and the boundary parts) in the reduced phase space based on the Brown-Kuchaˇr Formalism. In this work, we introduce specific asymptotically flat boundary conditions to make the variation of the physical Hamiltonian well-defined. Using these boundary conditions, we construct the boundary-preserving symmetries, including supertranslations and superrotations. The algebra of these symmetry generators is given by the Poisson brackets, which contains a center extension.