ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: Artamonov, V. A., Department of Algebra, Faculty of Mechanics and Mathematics, Moscow state university, 119899, Moscow, Russia Quantum polynomial algebra is a multiparameter deformation of an algebra of polynomials, i. e. it is the algebra of regular functions on a quantum affine space We assume that the multiparameters are in a general position. It is shown that projective modules of a rank ≥ 2 over this ring are free. If Λ, Λ′ are Morita-equivalent quantum polynomials and Λ is a general one, then Λ ≃ Λ′. If a general quantum polynomial algebra Λ is a skew polynomial extension and Λ is a skew polynomial extension either Λ ≃ Λ_{1}[X; α] or Λ ≃ Λ_{1}[X^{±1}; α] with an automorphism α, then Λ_{1} is a general quantum polynomial algebra.