On the Hall Algebra of Semigroup Representations over F1

Abstract

Let A be a finitely generated semigroup with 0. An A–module over F1 (also called an A–set), is a pointed set (M, ∗) together with an action of A. We define and study the Hall algebraHA of the category CA of finite A–modules. HA is shown to be the universal enveloping algebra of a Lie algebra nA, called the Hall Lie algebra of CA. In the case of the 〈t〉 the… (More)

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