40 research outputs found
Differential Calculi on Some Quantum Prehomogeneous Vector Spaces
This paper is devoted to study of differential calculi over quadratic
algebras, which arise in the theory of quantum bounded symmetric domains. We
prove that in the quantum case dimensions of the homogeneous components of the
graded vector spaces of k-forms are the same as in the classical case. This
result is well-known for quantum matrices.
The quadratic algebras, which we consider in the present paper, are
q-analogues of the polynomial algebras on prehomogeneous vector spaces of
commutative parabolic type. This enables us to prove that the de Rham complex
is isomorphic to the dual of a quantum analogue of the generalized
Bernstein-Gelfand-Gelfand resolution.Comment: LaTeX2e, 51 pages; changed conten