- Gazi University Journal of Science
- Volume:35 Issue:3
- Classification of 8-dimensional Nilsolitons by Symbolic Computation
Classification of 8-dimensional Nilsolitons by Symbolic Computation
Authors : Hülya KADIOĞLU
Pages : 1031-1049
Doi:10.35378/gujs.911475
View : 47 | Download : 12
Publication Date : 2022-09-01
Article Type : Research Paper
Abstract :In this paper, we develop an algorithm to classify 8 dimensional nilsolitons with simple nilsoliton derivation. We restrict our classifications to the nilsolitons corresponding to singular Gram matrix with nullity 1-3. This work can be considered as a continuation paper to our previous study where we introduced a procedure to classify algebras in dimension 8 that admit simple derivations and singular Gram matrices U. Having the singular Gram matrices, there exists infinitely many solutions to Uv =[1]_m , where the solutions are exactly the squares of the structure constants. Also, the structure constants have to satisfy the Jacobi identity for the algebra to be a Lie algebra. In our previous work, we did not introduce a procedure to create and solve the Jacobi identityinsert ignore into journalissuearticles values(s);. In this study, we take care of this issue by using computer algorithms for each index set. Thus, we complete classification of all 8 dimensional in-decomposable nilsolitons with the nullity of corresponding Gram matrix is in the set {0,1,2,3}. We provide several examples to illustrate the algorithm. For the implementation process of the newly introduced algorithm, we use MATLAB R2020b.Keywords : Solvable Lie algebras, Symbolic computation, Nilpotent Lie groups, Solvable Lie groups
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