Multivector Contractions Revisited, Part II

The theory of contractions of multivectors, and star duality, was reorganized in a previous article, and here we present some applications. First, we study inner and outer spaces associated to a general multivector M via the equations \(v \wedge M = 0\) $v\wedge M=0$ and \(v \mathbin {\lrcorner }M=0\) $v⌟M=0$ . They are then used to analyze special decompositions, factorizations and ‘carvings’ of M, to define generalized grades, and to obtain new simplicity criteria, including a reduced set of Plücker-like relations. We also discuss how contractions are related to supersymmetry, and give formulas for supercommutators of multi-fermion creation and annihilation operators.