New algebraic properties of biregular functions in 2n quaternionic variables

Abstract

In this article we exploit some general results on the tensor product of free resolutions to deduce important new algebraic properties of biregular functions in 2n quaternionic variables. In particular, we are able to construct a minimal resolution for the associated module and compute all the relevant graded Betti numbers.

§Dedicated to Richard Delanghe on the occasion of his 65th birthday. This article is dedicated, with friendship and admiration, to Professor Richard Delanghe, who has done so much, as a mathematician and as a leader, to further the work on Clifford Analysis around the world.

Keywords:

• Cauchy–Fueter operator
• Biregular function
• Syzygies

Keywords:

• MSC 2000: 30G35
• 16E05

Notes

§Dedicated to Richard Delanghe on the occasion of his 65th birthday. This article is dedicated, with friendship and admiration, to Professor Richard Delanghe, who has done so much, as a mathematician and as a leader, to further the work on Clifford Analysis around the world.