Supermanifold
In mathematics and mathematical physics, supermanifolds are generalizations of manifolds in which the algebra of functions includes both commuting and anticommuting variables. In the standard mathematical formulation, a smooth supermanifold is a locally ringed space whose structure sheaf is locally isomorphic to the tensor product of the ring of ordinary smooth functions C ∞ ( R p ) {\displaystyle C^{\infty }(\mathbb {R} ^{p})} and a Grassmann algebra Λ ( ξ 1 , … , ξ q ) {\displaystyle \Lambda (\xi _{1},\dots ,\xi _{q})} of the anticommuting variables.