This note gives a categorical development arising from a theorem of A. A. Klyachko relating the Lie operad to roots of unity. We examine the "substitude" structure on the groupoid C whose homsets are the cyclic groups. The roots of unity representations of the cyclic groups form a Lie algebra for a certain oplax monoidal structure on the category of linear representations of C.
|Number of pages||8|
|Journal||Georgian Mathematical Journal|
|Publication status||Published - 2002|
- Lie algebra
- cyclic group