AI 中文总结
该研究引入李代数同态的上同调维数和同调维数概念，建立其基本性质，获上同调维数链同伦刻画，并计算自由和阿贝尔李代数间同态的这些不变量。
AI 中文摘要
我们引入李代数同态的上同调维数和同调维数概念，扩展了群同态的相应不变量。建立其基本性质，包括在单同态、满同态、拉回、合成以及限制到像下的行为。还得到上同调维数的链同伦刻画，并明确计算自由和阿贝尔李代数之间同态的这些不变量。
英文摘要
We introduce the notions of the cohomological dimension and the homological dimension of Lie algebra homomorphisms, extending the corresponding invariants for group homomorphisms. We establish their basic properties, including their behavior under monomorphisms, epimorphisms, pullbacks, composition, and restriction to the image. We also obtain a chain homotopy characterization of the cohomological dimension and compute these invariants explicitly for homomorphisms between free and abelian Lie algebras.
Comments9 pages
