摘要
In this paper, we study selfinjective Koszul algebras of finite complexity. We prove that the complexity is a nonnegative integer when it is finite; and that the category Yt of modules with complexity less or equal to t, is resolving and coresolving. We show that for each 0 ≤ 1 ≤ m there exist a family of modules of complexity 1 parameterized by G（l, m）, the Grassmannian of l-dimensional subspaces of an m-dimensional vector space V, for the exterior algebra of V. Using complexity, we also give a new approach to the representation theory of a tame symmetric algebra with vanishing radical cube over an algebraically closed field of characteristic 0, via skew group algebra of a finite subgroup of SL（2, C） over the exterior algebra of a 2-dimensional vector space.
In this paper, we study selfinjective Koszul algebras of finite complexity. We prove that the complexity is a nonnegative integer when it is finite; and that the category Yt of modules with complexity less or equal to t, is resolving and coresolving. We show that for each 0 ≤ 1 ≤ m there exist a family of modules of complexity 1 parameterized by G（l, m）, the Grassmannian of l-dimensional subspaces of an m-dimensional vector space V, for the exterior algebra of V. Using complexity, we also give a new approach to the representation theory of a tame symmetric algebra with vanishing radical cube over an algebraically closed field of characteristic 0, via skew group algebra of a finite subgroup of SL（2, C） over the exterior algebra of a 2-dimensional vector space.
基金
Supported by NSFC #10671061
SRFDP #200505042004
the Cultivation Fund of the Key Scientific and Technical Innovation Project #21000115 of the Ministry of Education of China
