1. On Some Structural Components of Nilsolitons
- Author
-
Hulya Kadioglu
- Subjects
Jacobi identity ,Pure mathematics ,Structure constants ,Article Subject ,Rank (linear algebra) ,General Mathematics ,010102 general mathematics ,General Engineering ,Structure (category theory) ,010103 numerical & computational mathematics ,Engineering (General). Civil engineering (General) ,01 natural sciences ,Nilpotent ,symbols.namesake ,Simple (abstract algebra) ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Metric (mathematics) ,Lie algebra ,QA1-939 ,symbols ,TA1-2040 ,0101 mathematics ,Mathematics - 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. The 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.
- Published
- 2021