coregular action

Let $k$ be a field, $H$ a $k$-bialgebra and ${H}^{*}$ a dual bialgebra with duality $\u27e8,\u27e9:H\otimes {H}^{*}\to k$. The **left coregular action** is a Hopf action of $H$ on ${H}^{*}$ given by

$$(h,\varphi )\mapsto {R}_{h}(\varphi ):={\varphi}_{(1)}\u27e8h,{\varphi}_{(2)}\u27e9$$

The corresponding representation ${R}_{h}:H\to \mathrm{End}{H}^{*}$ 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)