Q.-S. Wu

HOMOLOGICAL INTEGRAL OF HOPF ALGEBRAS

The left and right homological integrals are introduced for a large class of infinite dimensional Hopf algebras. Using the homological integrals we prove a version of Maschkes theorem for infinite dimensional Hopf algebras. The generalization of Maschkes theorem and homological integrals are the keys to studying noetherian regular Hopf algebras of Gelfand-Kirillov dimension one.

Pre-balanced dualizing complexes

We study pre-balanced dualizing complexes over noncommutative complete semilocal algebras and prove an analogue of Van den Bergh’s theorem [VdB, 6.3]. The relationship between pre-balanced dualizing complexes and Morita dualities is studied. Some immediate applications to classical ring theory are also given.