On the Hall algebra of semigroup representations over \(\mathbb F _1\)

作者: Matt Szczesny

DOI: 10.1007/S00209-013-1204-3

关键词: Discrete mathematicsNilpotentHopf algebraGenerator (category theory)Lie algebraFinite groupPointed setMathematicsUniversal enveloping algebraHall algebra

摘要: Let \(\mathrm{A }\) be a finitely generated semigroup with 0. An }\)-module over \(\mathbb F _1\) (also called an }\)-set), is pointed set \((M,*)\) together action of }\). We define and study the Hall algebra H _{\mathrm{A }}\) category \(\mathcal C finite }\)-modules. shown to universal enveloping Lie \(\mathfrak n }}\), }}\). In case \(\langle t \rangle \)—the free monoid on one generator \), (or more precisely subcategory nilpotent \)-modules) isomorphic Kreimer’s Hopf rooted forests. This perspective allows us two new commutative operations also consider examples when quotient \) by congruence, \(G \cup \{ 0\}\) for group \(G\).

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