# nLab coregular action

Let $k$ be a field, $H$ a $k$-bialgebra and $H^*$ a dual bialgebra with duality $\langle, \rangle : H\otimes H^*\to k$. The left coregular action is a Hopf action of $H$ on $H^*$ given by

$(h,\phi) \mapsto R_h(\phi) := \phi_{(1)} \langle h, \phi_{(2)}\rangle$

The corresponding representation $R_h: H\to End H^*$ is called the left coregular representation. It is used in the definition of Heisenberg double.

Revised on August 25, 2011 00:26:24 by Zoran Škoda (161.53.130.104)