A chain rule formula for higher derivations and inverses of polynomial maps. Issue 7 (3rd July 2019)

• Record Type: Journal Article
• Authors: Maurischat, Andreas
• Is Part Of: Communications in algebra. Volume 47:Issue 7(2019)
• Page Start: 2617
• Page End: 2633
• Publication Date: 2019-07-03
• Subjects: Chain rule -- higher derivations -- polynomial automorphisms; 12H05 -- 13N15 -- 14R15; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1530243
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: The multidimensional chain rule formula for analytic functions and its generalization to higher derivatives perfectly work in the algebraic setting in characteristic zero. In positive characteristic one runs into problems due to denominators in these formulas. In this article we show a direct analog of these formulas using higher derivations which are defined in any characteristic. We also use these formulas to show how higher derivations to different coordinate systems are related to each other. Finally, we apply this to polynomial automorphisms in arbitrary characteristic and obtain a formula for the inverse of such a polynomial automorphism.