On Some Structural Components of Nilsolitons

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Kadıoğlu H.

Mathematical Problems In Engineering, vol.2021, no.2021, pp.1-6, 2021 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 2021 Issue: 2021
  • Publication Date: 2021
  • Doi Number: 10.1155/2021/5540584
  • Journal Name: Mathematical Problems In Engineering
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Page Numbers: pp.1-6
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, we study nilpotent Lie algebras that admit nilsoliton metric with simple pre-Einstein derivation. Given a Lie algebra

η, we would like to compute as much of its structure as possible. (e structural components we consider in this study are the

structure constants, the index, and the rank of the nilsoliton derivations. For this purpose, we prove necessary or sufficient

conditions for an algebra to admit such metrics. Particularly, we prove theorems for the computation of the Jacobi identity for a

given algebra so that we can solve the system of the equation(s) and find the structure constants of the nilsoliton