an:01584195
Zbl 0962.05012
Clarke, Francis; Hunton, John; Ray, Nigel
Extensions of umbral calculus. II: Double delta operators, Leibniz extensions and Hattori-Stong theorems
EN
Ann. Inst. Fourier 51, No. 2, 297-336 (2001).
0373-0956 1777-5310
2001
j
05A40 55N22
umbral calculus; Hattori-Stong theorems; polynomial algebras; delta operators; power series; algebraic topology
Summary: ``We continue our programme of extending the Roman-Rota umbral calculus to the setting of delta operators over a graded ring \(E_{*}\) with a view to applications in algebraic topology and the theory of formal group laws. We concentrate on the situation where \(E_{*}\) is free of additive torsion, in which context the central issues are number-theoretic questions of divisibility. We study polynomial algebras which admit the action of two delta operators linked by an invertible power series, and make related constructions motivated by the Hattori-Stong theorem of algebraic topology. Our treatment is couched purely in terms of the umbral calculus, but inspires novel topological applications. In particular we obtain a generalised form of the Hattori-Stong theorem.''
For Part I see \textit{N. Ray} [Adv. Math. 61, 49-100 (1986; Zbl 0631.05002)].
0631.05002