We define the Lie transformation algebra of a (not necessarily associative) monoid object in a -linear symmetric monoidal category , where is a field. When is associative and satisfies certain conditions, we describe explicity the Lie transformation algebra and inner derivations of . Additionally, we also show that derivations preserve the nucleus of the monoid .
Cite this article
Abhishek Banerjee, On the Lie transformation algebra of monoids in symmetric monoidal categories. Rend. Sem. Mat. Univ. Padova 131 (2014), pp. 151–157DOI 10.4171/RSMUP/131-8