论文标题
有限posets的免费前代数
Free pre-lie algebras of finite posets
论文作者
论文摘要
在本文中，我们首先回想起有限连接的拓扑空间的扭曲的前代数结构。然后，我们构建了相应的非社交置换性共同体，并证明有限POSET的同构类别产生的矢量空间是一个免费的前代代数，并且是一种无共同的非缔合性煤层。最后，我们在非缔合性置换产品和提议的非求职置换性共同点之间给出了明确的二元性。最后，我们证明本文的结果对于有限连接的拓扑空间仍然是正确的。
In this paper, we first recall the construction of a twisted pre-Lie algebra structure on the species of finite connected topological spaces. Then we construct the corresponding nonassociative permutative coproduct, and we prove that the vector space generated by isomorphism classes of finite posets is a free pre-Lie algebra and is a co-free non-associative permutative coalgebra. In the end, we give an explicit duality between the non-associative permutative product and the proposed non-associative permutative coproduct. Finally, we prove that the results in this paper remain true for the finite connected topological spaces.
