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On the Cohomology of Lie Algebras with an Invariant Inner Product
Algebras and Representation Theory ( IF 0.5 ) Pub Date : 2021-06-17 , DOI: 10.1007/s10468-021-10061-x Alice Fialowski , Michael Penkava
中文翻译:
具有不变内积的李代数的上同调
更新日期:2021-06-17
Algebras and Representation Theory ( IF 0.5 ) Pub Date : 2021-06-17 , DOI: 10.1007/s10468-021-10061-x Alice Fialowski , Michael Penkava
In this work we consider the moduli space of all noncommutative metric Lie algebras, having a nondegenerate symmetric invariant bilinear form, over \(\mathbb C\) and \(\mathbb R\) up to dimension 5 and all metric Lie algebras over \(\mathbb C\) in dimension 6. We introduce cyclic and reduced cyclic cohomology to identify their metric deformations.
中文翻译:
具有不变内积的李代数的上同调
在这项工作中,我们考虑所有非对易度量李代数的模空间,具有非退化对称不变双线性形式,在\(\mathbb C\)和\(\mathbb R\)上直到维度 5 和所有度量李代数在\ (\mathbb C\)在第 6 维。我们引入循环和约简循环上同调来识别它们的度量变形。