Jordan superalgebra
Urs Schreiber
superalgebra and (synthetic ) supergeometry
The notion of Jordan superalgebra is the analog in superalgebra/supergeometry of that of Jordan algebra:
A Jordan superalgebra is a supercommutative superalgebra with underlying -graded algebra , where:
is an ordinary Jordan algebra,
is a -bimodule with a “Lie bracket-like” product into ,
satisfying a super Jordan identity.
Simple Jordan superalgebras over an algebraically closed field of characteristic 0 were classified by Kac (Kac 77). The only...