Graded Lie algebra
= Graded Lie algebra
A <graded Lie algebra> has a <graded Lie bracket> preserving total degree, with $[u,v]=-(-1)^{|u||v|}[v,u]$ and $[u,[v,w]]=[[u,v],w]+(-1)^{|u||v|}[v,[u,w]]$ for homogeneous vectors in the indicated degrees. A <Gerstenhaber algebra> uses this sign rule after shifting degrees by one.