# On the Lie transformation algebra of monoids in symmetric monoidal categories

### Abhishek Banerjee

Indian Institute of Science, Bangalore, India

## Abstract

We define the Lie transformation algebra of a (not necessarily associative) monoid object $A$ in a $K$-linear symmetric monoidal category $(C,\otimes,1)$, where $K$ is a field. When $A$ is associative and satisfies certain conditions, we describe explicity the Lie transformation algebra and inner derivations of $A$. Additionally, we also show that derivations preserve the nucleus of the monoid $A$.

## Cite this article

Abhishek Banerjee, On the Lie transformation algebra of monoids in symmetric monoidal categories. Rend. Sem. Mat. Univ. Padova 131 (2014), pp. 151–157

DOI 10.4171/RSMUP/131-8