Classification of 3-dimensional Hom-Lie algebras

• For any n-dimensional Hom-Lie algebra, a system of polynomial equations is obtained from the Hom-Jacobi identity, containing both structure constants of the skew-symmetric bilinear map and constants describing the twisting linear endomorphism. The equations are linear in the constants representing the endomorphism and non-linear in the structure constants. The space of possible endomorphisms has minimum dimension 6, and we describe the possible endomorphisms in that case. We further give families of 3-dimensional Hom-Lie algebras arising from a general nilpotent linear endomorphism constructed upto isomorphism.

Subject headings

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

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

Keyword

Polynomials

3-dimensional

Bilinear map

Lie Algebra

Nilpotent

Non linear

Skew-symmetric

Structure constants

System of polynomial equations

Mathematics/Applied Mathematics

matematik/tillämpad matematik

Publication and Content Type

ref (subject category)

kon (subject category)