Quantum supergroups of $GL(n|m)$ type: differential forms, Koszul complexes and Berezinians

Volodymyr Lyubashenko, A. Sudbery

We introduce and study the Koszul complex for a Hecke $R$-matrix. Its cohomologies, called the Berezinian, are used to define quantum superdeterminant for a Hecke $R$-matrix. Their…