On the Lie transformation algebra of monoids in symmetric monoidal categories. (English) Zbl 1336.18003

Let \(K\) be a field. The main goal of this paper is to extend the theory of inner derivations for nonassociative algebras developed by R. D. Schafer [Bull. Am. Math. Soc. 55, 769–776 (1949; Zbl 0033.34803)] to monoids over a \(K\)-linear symmetric monoidal category. Moreover, if \(A\) is an associative monoid, the author describes the Lie transformation algebra (Proposition 2.2) and inner derivations of \(A\) (Proposition 2.3). Finally, he shows (Proposition 2.5) that derivations preserve the nucleus of the monoid \(A\).


18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras)


Zbl 0033.34803
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