On tensor products and almost split sequences for Scott lattices over group rings
On tensor products and almost split sequences for Scott lattices over group rings
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关于群环上斯科特格的张量积和几乎分裂序列
DOI：
10.1016/j.jalgebra.2022.02.008
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发表时间：
2022
影响因子：
0.9
通讯作者：
Kawata Shigeto
中科院分区：
文献类型：
--
作者：
Ayumu Inoue;Naoki Kimura;Ryo Nikkuni and Kouki Taniyama;Inoue Ayumu;井上 歩;井上 歩;井上 歩;井上 歩;井上 歩;井上 歩;Ayumu Inoue;Hiroshi Goda;井上 歩;Kawata Shigeto
设G是G的一个有限群，Q是G的一个p子群，设O是一个特征为0的完整离散赋值环，特征为p的代数闭残类域。我们证明了对于一个不可分解的O - G格L，其Q源为T，其几乎分裂序列a （S (Q)）终止于顶点为Q的Scott格S (Q)，张量序列L⊗O A （S (Q)）是终止于L的几乎分裂序列A (L)与分裂序列当且仅当L是几乎不可约且T是分裂迹格时的直接和。
Let G be a finite group and Q a p-subgroup of G. Let O be a complete discrete valuation ring of characteristic zero with algebraically closed residue class field of characteristic p. We show that for an indecomposable O G-lattice L with a Q-source T and the almost split sequence A (S (Q)) terminating in the Scott lattice S (Q) with vertex Q, the tensor sequence L⊗ O A (S (Q)) is a direct sum of the almost split sequence A (L) terminating in L and a split sequence if and only if L is virtually irreducible and T is a splitting trace lattice.