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Distributive laws between the operads Lie and Com
International Journal of Algebra and Computation ( IF 0.8 ) Pub Date : 2020-07-17 , DOI: 10.1142/s021819672050054x
Murray Bremner 1 , Vladimir Dotsenko 2
Affiliation  

Using methods of computer algebra, especially, Gröbner bases for submodules of free modules over polynomial rings, we solve a classification problem in theory of algebraic operads: we show that the only nontrivial (possibly inhomogeneous) distributive law between the operad of Lie algebras and the operad of commutative associative algebras is given by the Livernet–Loday formula deforming the Poisson operad into the associative operad.

中文翻译:

Lie 和 Com 之间的分配规律

使用计算机代数的方法,特别是多项式环上自由模子模的 Gröbner 基,我们解决了代数操作数理论中的分类问题:我们证明了李代数的操作数与交换结合代数的操作数由将泊松操作数变形为结合操作数的 Livernet-Loday 公式给出。
更新日期:2020-07-17
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