Hopf代数作用的几个传递性质

Some Hereditary Properties of Hop f Algebra Actions

设Ｈ是域ｋ上的有限维Ｈｏｐｆ代数，Ａ是左Ｈ模代数，本文得到：当Ｈ半单时，若Ａ有Ｋｒｕｌｌ维数，则ＡＨ也有，且ＫｄｉｍＡＨ≤ＫｄｉｍＡ；当Ａ是仿射ＰＩ代数时，且Ａ含这为１的元素，对ｐ∈Ｓｐｅｃ（ＡＨ），有ＧＫ（ＡＨ／Ｐ）＝ｃｌＫｄｉｍ（ＡＨ／Ｐ）。

Let H be a finite-dimensional Hop f algebra and A left H-module algebra, if H is semisimple and A has krull dimension, then AH also has krull dimension and Kdim AH≤KdimA. If A is affine PI algebra with an element of trace 1 and p∈Spec(AH),thenGK(AH/P)=clKdim(A'H/p).