Bracket algebra

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 ["L"] is the supersymmetric algebra, the bracket algebra Bracket ["L"] of dimension "n" over the field "K" is the quotient of the algebra Brace{"L"} obtained by imposing the congruence relations below, where "w", "w"', ..., "w" are any monomials in Super ["L"] :

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

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Bracket algebra

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