Differential Calculi on Some Quantum Prehomogeneous Vector Spaces

Abstract

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.

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References in corpus (5)

• Differential forms via the Bernstein-Gelfand-Gelfand resolution for quantized irreducible flag manifolds
• Rings of skew polynomials and Gel'fand-Kirillov conjecture for quantum groups
• Integral Intertwining Operators and Complex Powers of Differential ($q-$Difference) Operators
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Cited by in corpus (1)

• Differential forms via the Bernstein-Gelfand-Gelfand resolution for quantized irreducible flag manifolds