置换面体上的自由代数结构
Free algebraic structures on the permutohedra
摘要：
三树型代数是一类结合代数，由F. Chapoton和J. - L. Loday和第三作者，为了描述与Stasheff多面体有关的操作。置换面所张成的向量空间$\st$具有三树型双代数的自然结构，证明了它作为三树型代数是自由的，并有一个基。我们的结果意味着带有置换面体的余边界映射的余代数$\st$的本原元的子空间是自由仙人掌代数。
英文摘要：
Tridendriform algebras are a type of associative algebras, introduced independently by F. Chapoton and by J.-L. Loday and the third author, in order to describe operads related to the Stasheff polytopes. The vector space $\st$ spanned by the faces of permutohedra has a natural structure of tridendriform bialgebra, we prove that it is free as a tridendriform algebra and exhibit a basis. Our result implies that the subspace of primitive elements of the coalgebra $\st$ , equipped with the coboundary map of permutohedra, is a free cacti algebra.
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