有限群稳定模范畴的Bousfield等价

Bousfield Equivalence of Stable Module Category for Finite Group

考虑有限群稳定模范畴的Bousfield等价关系,证明了若H是G的强p-嵌入子群,则两个有限生成不可分解kG-模(kH-模)是Bousfield等价的当且仅当其Green对应是Bousfield等价的,且Green对应诱导了Stmod(kG)的全体Bousfield等价类与Stmod(kH)的全体Bousfield等价类之间的一一对应.

The author considered the Bousfield equivalence relationship of the stable module category for a finite group, and proved that, if H was a strongly p-embedded subgroup of G, then two finitely generated indecomposable kG-modules （kH-modules） were Bousfield equivalent if and only if their Green correspondents were Bousfield equivalent, in addition, Green correspondence induced a one-to-one correspondence between Bousfield equivalence classes of Stmod（kG） and those of Stmod（kH）.