Twists of quantum Borel algebras

Abstract

We classify Drinfeld twists for the quantum Borel subalgebra uq(b) in the Frobenius-Lusztig kernel uq(g), where g is a simple Lie algebra over C and q an odd root of unity. More specifically, we show that alternating forms on the character group of the group of grouplikes for uq(b) generate all twists for uq(b), under a certain algebraic group action. This implies a simple classification of Hopf algebras whose categories of representations are tensor equivalent to that of uq(b). We also show that cocycle twists for the corresponding De Concini-Kac algebra are in bijection with alternating forms on the aforementioned character group.