Cartan Form Exterior Super Algebra
Each element of the super-algebra is of the form
a(p+1) + db(p)
a is a p + 1 form
b is a p-form
d = Cartan exterior derivative that is nilpotent
d^2 = 0
[a(p+1) + db(p)] + [c(p+1) + de(p)] = [a(p+1) + c(p+1)] + d[b(p) + e(p)]
Exterior multiplication law
[a(p+1) + db(p)]/\[c(p+1) + de(p)]
= a(p+1)/\c(p+1) + d[a(p+1)/\e(p) + b(p)/\c(p+1)]
In n-dim space the largest non-zero p-form is an n-form.
Is this well-known or did I just invent it?
Ref. p. 877 "The Road to Reality" by Roger Penrose