In this paper, we propose a method to obtain the syzygies of the Dirac complex defined on abstract vector variables. We propose a generalized theory of differential forms which acts as a de Rham-like sequence for the Dirac complex and we show that closure in this complex is equivalent to the syzygies for the Dirac complex.
"The Dirac Complex on Abstract Vector Variables: Megaforms." Experiment. Math. 12 (3) 351 - 364, 2003.