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

Banerjee, Abhishek

Rend. Semin. Mat. Univ. Padova 131, 151-157 (2014).

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 \(A\).

Reviewer: J. N. Alonso Alvarez (Vigo)

MSC:

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

Keywords:

inner derivations; Lie transformation algebra

Citations:

Zbl 0033.34803

References:

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