The Drinfeld–Lusztig Double of a Group Algebra

The following definition is a particular case of a general construction due to Drinfeld [21], which applies to any Hopf k-algebra (see Section 18.3 below) and its k-dual. Here we only consider the particular case of the Hopf algebra kG (G a finite group) and its dual F(G, k). In a first part, we endow the algebra DkG := F(G, k) ⋊G with the structure of a k-algebra, which is due to Lusztig [36, §2].