nLab
coregular action

Let k be a field, H a k-bialgebra and H * a dual bialgebra with duality ,:HH *k. The left coregular action is a Hopf action of H on 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 * 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)