Christian Lomp (Porto), On the construction of integrable differential calculi on some non-commutative algebras.

Abstract:

An integrable differential calculus on an algebra A (in the sense of Brzezinski) is an n-dimensional connected differential calculus \Omega=A\oplus \Omega^1 \oplus \cdots \oplus \Omega^n with differential d, such that the de Rham complex (\Omega^*, d) is isomorphic to a certain complex, called the complex of integral forms. In this talk we will discuss the construction of such differential calculi for some non-commutative algebras, including some Hopf algebras, quantum exterior algebras and Manin's quantum space.