Bracket algebra

In mathematics, a bracket algebra is an algebraic system that connects the notion of a supersymmetry algebra with a symbolic representation of projective invariants.
Given that L is a proper signed alphabet and Super is the supersymmetric algebra, the bracket algebra Bracket of dimension n over the field K is the quotient of the algebra Brace obtained by imposing the congruence relations below, where w, w',..., w" are any monomials in Super:

= 0 if length ≠ n
... = 0 whenever any positive letter a of L occurs more than n times in the monomial....
Let... be a monomial in Brace in which some positive letter a occurs more than n times, and let b, c, d, e,..., f, g be any letters in L.