On Classification of (n+1)-Dimensional n-Hom-Lie Algebras with Nilpotent Twisting Maps

• The aim of this work is to study properties of n-Hom-Lie algebras in dimension n+1 allowing to explicitly find them and differentiate them, to eventually classify them. Some specific properties of (n+1) -dimensional n-Hom-Lie algebra such as nilpotence, solvability, center, ideals, derived series and central descending series are studied, the Hom-Nambu-Filippov identity for various classes of twisting maps in dimension n+1 is considered, and systems of equations corresponding to each case are described. All 4-dimensional 3-Hom-Lie algebras with some of the classes of twisting maps are computed in terms of structure constants as parameters and listed in the way emphasising the number of free parameters in each class, and also some detailed properties of the Hom-algebras are obtained.

Subject headings

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

Keyword

Hom-algebra

n-Hom-Lie algebra

Mathematics/Applied Mathematics

matematik/tillämpad matematik

Publication and Content Type

ref (subject category)

kon (subject category)