nLab
coregular action

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

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

The corresponding representation R h:HEndH *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)