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The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (2016R1A2B4011321 and 2016R1A5A1008055). The second, third and fourth authors were partially supported by the grant MINECO MTM2015-63612-P.

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Luzon, AnaAuthorFelipe Prieto-Martinez, L.Corresponding Author

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June 9, 2019
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Finite and infinite dimensional Lie group structures on Riordan groups

Publicated to:Advances In Mathematics. 319 522-566 - 2017-10-15 319(), DOI: 10.1016/j.aim.2017.08.033

Authors: Cheon, Gi-Sang; Luzon, Ana; Moron, Manuel A; Felipe Prieto-Martinez, L; Song, Minho

Affiliations

Inst Matemat Interdisciplinar, Madrid, Spain - Author
Sungkyunkwan Univ, Suwon 16419, South Korea - Author
Univ Automa Madrid, Madrid, Spain - Author
Univ Complutense Madrid, Madrid, Spain - Author
Univ Politecn Madrid, Madrid, Spain - Author
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Abstract

We introduce a Frechet Lie group structure on the Riordan group. We give a description of the corresponding Lie algebra as a vector space of infinite lower triangular matrices. We describe a natural linear action induced on the Frechet space K-N by any element in the Lie algebra. We relate this to a certain family of bivariate linear partial differential equations. We obtain the solutions of such equations using one-parameter groups in the Riordan group. We show how a particular semidirect product decomposition in the Riordan group is reflected in the Lie algebra. We study the stabilizer of a formal power series under the action induced by Riordan matrices. We get stabilizers in the fraction field K((x)) using bi-infinite representations. We provide some examples. The main tool to get our results is the paper [18] where the Riordan group was described using inverse sequences of groups of finite matrices. (C) 2017 Elsevier Inc. All rights reserved.

Keywords

ArraysExponential mapFinite dimensional riordan groupsFrechet lie groupLie algebraMatricesPolynomialsRiordan groupStabilizers

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Advances In Mathematics due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2017, it was in position 33/310, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics. Notably, the journal is positioned above the 90th percentile.

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 1.75. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 14, 2024)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

  • Weighted Average of Normalized Impact by the Scopus agency: 1.15 (source consulted: FECYT Feb 2024)
  • Field Citation Ratio (FCR) from Dimensions: 7.36 (source consulted: Dimensions Jul 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-07-15, the following number of citations:

  • WoS: 12
  • Scopus: 13

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-07-15:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 8 (PlumX).

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Republic of Korea.

the author responsible for correspondence tasks has been PRIETO MARTINEZ, LUIS FELIPE.