论文标题
线性源可逆双模型和绿色对应关系
Linear source invertible bimodules and Green correspondence
论文作者
论文摘要
我们表明，绿色对应诱导了线性源PICARD组$ \ MATHCAL {l}（b）$ b $的有限组代数的$ \ MathCal {l}（b）$引起的注射组同构，直线源PICARD组$ \ MATHCAL $ \ MATHCAL {l}（l}（l}）（c）$ c $ c $是$ c $ brauer的brauer of $ b $。此同态映射琐碎的源PICARD组$ \ MATHCAL {t}（b）$ $ to to to Trivial Source PICARD组$ \ MATHCAL {t}（t}（c）$。我们进一步表明，内皮源源PICARD组$ \ MATHCAL {E}（b）$是根据$ b $的缺陷组进行的，并且当$ b $具有正常缺陷组$ \ MATHCAL $ \ MATHCAL {E}（b）= \ MATHCAL = \ MATHCAL {l}（l}（b）$。最后，我们证明，任何可逆的$ b $ bimodule的排名都受$ b $的界限。
We show that the Green correspondence induces an injective group homomorphism from the linear source Picard group $\mathcal{L}(B)$ of a block $B$ of a finite group algebra to the linear source Picard group $\mathcal{L}(C)$, where $C$ is the Brauer correspondent of $B$. This homomorphism maps the trivial source Picard group $\mathcal{T}(B)$ to the trivial source Picard group $\mathcal{T}(C)$. We show further that the endopermutation source Picard group $\mathcal{E}(B)$ is bounded in terms of the defect groups of $B$ and that when $B$ has a normal defect group $\mathcal{E}(B)=\mathcal{L}(B)$. Finally we prove that the rank of any invertible $B$-bimodule is bounded by that of $B$.
