Twisted Calabi-Yau property of right coideal subalgebras of quantized enveloping algebras

Suppose that U is the quantized enveloping algebra of some finite-dimensional semisimple Lie algebra g and C is a right coideal subalgebra of U such that the group-like elements contained in C form a group. Then C is Artin-Schelter regular and twisted Calabi-Yau. The Nakayama automorphism of C is also determined if C is contained in the Borel part U⩾0.