In mathematics, a bracket algebra is an algebraic system that connects the notion of a
supersymmetry algebra In theoretical physics, a supersymmetry algebra (or SUSY algebra) is a mathematical formalism for describing the relation between bosons and fermions. The supersymmetry algebra contains not only the Poincaré algebra and a compact subalgebra of int ...
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 obtained by imposing the congruence relations below, where ''w'', ''w, ..., ''w''" are any monomials in Super
'L''
# = 0 if length(''w'') ≠ ''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''.
See also
*
Bracket ring In mathematics invariant theory, the bracket ring is the subring of the ring of polynomials ''k'' 'x''11,...,''x'dn''generated by the ''d''-by-''d'' minors of a generic ''d''-by-''n'' matrix (''x'ij'').
The bracket ring may be regarded as th ...
References
*.
*{{Citation , last1 = Huang , first1 = Rosa Q. , last2 = Rota , first2 = Gian-Carlo , last3 = Stein , first3 = Joel A. , year = 1990 , title = Supersymmetric Bracket Algebra and Invariant Theory , periodical = Acta Applicandae Mathematicae , volume = 21 , issue = 1–2 , pages = 193–246 , publisher = Kluwer Academic Publishers , doi = 10.1007/BF00053298, s2cid = 189901418 .
Invariant theory
Algebras