The Dirac Complex on Abstract Vector Variables: Megaforms

Abstract

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.

Keywords:

• Complexes of hypercomplex operators
• Dirac operator
• differential forms
• radial algebra
• syzygies