Finite and infinite dimensional Lie group structures on Riordan groups
type: Item
instance of: scholarly article
title: Finite and infinite dimensional Lie group structures on Riordan groups
zbMATH Open document ID: 1378.22013
author: Gi-Sang Cheon
author: Ana Luzón
author: Min Ho Song
author: Manuel A. Morón
author: L. Felipe Prieto-Martinez
published in: Advances in Mathematics
publication date: 2017-09-19T00:00:00Z
review text: The paper under review introduces a Frechet Lie group structure on the Riordan group and describes the corresponding Lie algebra as a vector space of infinite lower triangular matrices. Any element of this Lie algebra induces a natural linear action on the Frechet space which turns out to be related to a certain family of bivariate linear partial differential equations. One-parameter subgroups of the Riordan group are then used to solve these equations. The paper also studies the Toeplitz-Lagrange decomposition of the Riordan group into a semidirect product and stabilizer of formal power series and of Laurent series under the action induced by Riordan matrices.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 22E66
Mathematics Subject Classification ID: 43A80
Mathematics Subject Classification ID: 20H99
Mathematics Subject Classification ID: 05A05
zbMATH DE Number: 6776233
zbMATH Keywords: Riordan group
zbMATH Keywords: Frechet Lie group
zbMATH Keywords: Lie algebra
zbMATH Keywords: exponential map
zbMATH Keywords: stabilizer
zbMATH Keywords: bivariate linear partial differential equation
Wikidata QID: Q115362010
MaRDI profile type: Publication
full work available at URL: j.aim.2017.08.033
OpenAlex ID: W2752891018
cites work: Algebra, geometry, and topology of the substitution group of formal power series
cites work: Structural properties of Riordan matrices and extending the matrices
cites work: A \(q\)-analogue of the Riordan group
cites work: The elements of finite order in the Riordan group over the complex field
cites work: Q3994935
cites work: Overview on Heisenberg-Weyl algebra and subsets of Riordan subgroups
cites work: The Sheffer group and the Riordan group
cites work: The Lie theory of connected pro-Lie groups. A structure theory for pro-Lie algebras, pro-Lie groups, and connected locally compact groups
cites work: Pro-Lie groups which are infinite-dimensional Lie groups
cites work: Some algebraic structure of the Riordan group
cites work: Substitution Groups of Formal Power Series
cites work: Q4360299
cites work: Q4338015
cites work: Iterative processes related to Riordan arrays: the reciprocation and the inversion of power series
cites work: Some inverse limit approaches to the Riordan group
cites work: Identities induced by Riordan arrays
cites work: Complementary Riordan arrays
cites work: Ultrametrics, Banach's fixed point theorem and the Riordan group
cites work: Riordan matrices in the reciprocation of quadratic polynomials
cites work: Bivariate delta-evolution equations and convolution polynomials: Computing polynomial expansions of solutions
cites work: On Some Alternative Characterizations of Riordan Arrays
cites work: Q3724586
cites work: Q3998356
cites work: Pascal triangles, Catalan numbers and renewal arrays
cites work: Lie groups. An introduction through linear groups
cites work: The Riordan group
cites work: Riordan arrays and combinatorial sums
cites work: Q4236280
DOI: 10.1016/J.AIM.2017.08.033
description: scientific article