On Riordan groups involving formal semi-Laurent series and their Lie group structure

2025/09/04 by Bugajewski, Dariusz, Bugajewski, Dawid, Gan, Xiao-Xiong +1
#17B65 #22E66 #58B10 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 13F25 #Secondary: 13J05

paper · doi:10.48550/arxiv.2509.04160

Abstract

The main goal of this paper is to introduce and to investigate properties of generalized Riordan arrays and generalized Riordan groups that involve formal semi-Laurent series. In particular, we focus on the problem of isomorphy of generalized Riordan groups with the classical Riordan groups giving the negative answer to this problem. We also examine infinite dimensional Lie group structure of the group of generalized Riordan arrays.

Citations

• Bi-infinite Riordan matrices: a matricial approach to multiplication and composition of Laurent series
• Topology and geometry of the general composition of formal power series -- towards Fréchet-Lie group-like formalism
• Characteristic Curves and the exponentiation in the Riordan Lie group: A connection through examples
• On composition and Right Distributive Law for formal power series of multiple variables
• The inverse and the composition in the set of formal Laurent series

Related

• Riordan Groups in higher Dimensions
• The Multiple Riordan Group and the Multiple Riordan Semigroup
• On the Group of Almost-Riordan Arrays
• Finding an Isomorphism between the Riordan Group and a Subgroup of the Double Riordan Group
• Generalized Riordan arrays and zero generalized Pascal matrices