Rendiconti del Seminario Matematico della Università di Padova


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Volume 131, 2014, pp. 151–157
DOI: 10.4171/RSMUP/131-8

Published online: 2014-06-08

On the Lie transformation algebra of monoids in symmetric monoidal categories

Abhishek Banerjee[1]

(1) Indian Institute of Science, Bangalore, India

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 $A$.

Keywords: Inner derivations, Lie transformation algebra

Banerjee Abhishek: On the Lie transformation algebra of monoids in symmetric monoidal categories. Rend. Sem. Mat. Univ. Padova 131 (2014), 151-157. doi: 10.4171/RSMUP/131-8