scholarly journals Computational methods for nilsoliton metric Lie algebras I

2013 ◽  
Vol 50 ◽  
pp. 350-373 ◽  
Author(s):  
Hülya Kadioglu ◽  
Tracy L. Payne
Keyword(s):  
Lie Algebras ◽  
Computational Methods ◽  
Nilsoliton Metric

scholarly journals Coclosed G2-structures inducing nilsolitons

2018 ◽  
Vol 30 (1) ◽  
pp. 109-128 ◽  
Author(s):  
Leonardo Bagaglini ◽  
Marisa Fernández ◽  
Anna Fino
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Complex Structure ◽  
Almost Complex Structure ◽  
Nilpotent Lie Algebras ◽  
Almost Complex ◽  
Metric Structures ◽  
Trivial Center ◽  
Nilsoliton Metric

Abstract We show obstructions to the existence of a coclosed {\mathrm{G}_{2}} -structure on a Lie algebra {\mathfrak{g}} of dimension seven with non-trivial center. In particular, we prove that if there exists a Lie algebra epimorphism from {\mathfrak{g}} to a six-dimensional Lie algebra {\mathfrak{h}} , with the kernel contained in the center of {\mathfrak{g}} , then any coclosed {\mathrm{G}_{2}} -structure on {\mathfrak{g}} induces a closed and stable three form on {\mathfrak{h}} that defines an almost complex structure on {\mathfrak{h}} . As a consequence, we obtain a classification of the 2-step nilpotent Lie algebras which carry coclosed {\mathrm{G}_{2}} -structures. We also prove that each one of these Lie algebras has a coclosed {\mathrm{G}_{2}} -structure inducing a nilsoliton metric, but this is not true for 3-step nilpotent Lie algebras with coclosed {\mathrm{G}_{2}} -structures. The existence of contact metric structures is also studied.

A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods.

1973 ◽  
Vol 136 (3) ◽  
pp. 461
Author(s):  
P. Holgate ◽  
Johan G. F. Belinfante ◽  
Bernard Kolman
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Computational Methods

scholarly journals On Some Structural Components of Nilsolitons

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Hulya Kadioglu
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Jacobi Identity ◽  
Sufficient Conditions ◽  
Structural Components ◽  
Nilpotent Lie Algebras ◽  
Structure Constants ◽  
Nilsoliton Metric

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.

A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods.

1991 ◽  
Vol 56 (194) ◽  
pp. 886
Author(s):  
Huib-Jan Imbens ◽  
Johan G. F. Belinfante ◽  
Bernard Kolman
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Computational Methods
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