一类可解保积Hom-李代数的确定

The Determination of a Class of Solvable Multiplicative Hom-Lie Algebras

摘要: 利用幂零李代数Q_2n及其自同构α的形变，得到幂零保积Hom-李代数（Q_2n，，'，α）.研究并确定了以幂零保积Hom-李代数（Q_2n，，'，α）为幂零根基的有限维不可分解的可解保积Hom-李代数（L，，'，σ）.结果表明Hom-李代数（L，，'，σ）的维数为dim Q_2n+1.

Abstract: By the deformation of nilpotent Lie algebra Q_2n and its automorphism α, nilpotent multiplicative Hom-Lie algebra (Q_2n, , ', α) is obtained. All finite-dimensional indecomposable solvable multiplicative Hom-Lie algebras (L, , ', σ), having the nilpotent multiplicative Hom-Lie algebra (Q_2n, , ', α) as the nilradical, are studied and determined. It shows that the dimension of Hom-Lie algebra (L, , ', σ) is dimQ_2n+1.