Hopf monoids in the category of species

被引：21
作者：
Aguiar, Marcelo [1 ]
Mahajan, Swapneel [2 ]
机构：
[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
[2] Indian Inst Technol Mumbai, Dept Math, Bombay 400076, Maharashtra, India
来源：
HOPF ALGEBRAS AND TENSOR CATEGORIES | 2013年 / 585卷
基金：
美国国家科学基金会;
关键词：
Species; Hopf monoid; Lie monoid; antipode; Hadamard product; partition; composition; linear order; simple graph; generalized permutahedron; Tits product; group-like; primitive; functional calculus; characteristic operation; Hopf power; Eulerian idempotent; Dynkin quasi-idempotent; Garsia-Reutenauer idempotent; Poincare-Birkhoff-Witt; Cartier-Milnor-Moore; HOCHSCHILD HOMOLOGY; ALGEBRAS; DECOMPOSITION; IDEMPOTENTS; ELEMENTS; LIE;
D O I：
10.1090/conm/585/11665
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A Hopf monoid (in Joyal's category of species) is an algebraic structure akin to that of a Hopf algebra. We provide a self-contained introduction to the theory of Hopf monoids in the category of species. Combinatorial structures which compose and decompose give rise to Hopf monoids. We study several examples of this nature. We emphasize the central role played in the theory by the Tits algebra of set compositions. Its product is tightly knit with the Hopf monoid axioms, and its elements constitute universal operations on connected Hopf monoids. We study analogues of the classical Eulerian and Dynkin idempotents and discuss the Poincare-Birkhoff-Witt and Cartier-Milnor-Moore theorems for Hopf monoids.
引用
收藏
页码：17 / +
页数：5
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