Bijections of silting complexes and derived Picard groups
نویسندگان
چکیده
We introduce a method that produces bijection between the posets silt − A $\textrm {{{\bf silt}}-}{A}$ and B silt}}-}{B}$ formed by isomorphism classes of basic silting complexes over finite-dimensional k $k$ -algebras $A$ $B$ , lifting to two [ X ] $k[\![X]\!]$ -orders which are isomorphic as rings. apply this class algebras generalising Brauer graph weighted surface algebras, showing their multiplicity-independent in most cases. Under stronger hypotheses, we also prove existence large subgroups derived Picard groups well multiplicity-invariance TrPicent ${\operatorname{\bf TrPicent}}$ . As an application modular representation theory finite groups, show if C $C$ blocks with | IBr ( ) = $|\operatorname{IBr}(B)|=|\operatorname{IBr}(C)|$ whose defect either both cyclic, dihedral or quaternion, then tilt tilt}}-}{B}$ tilt}}-}{C}$ (except, possibly, quaternion case 2 $|\operatorname{IBr}(B)|=2$ ≅ TrPicent}}(B)\cong {\operatorname{\bf TrPicent}}(C)$ cases ).
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2022
ISSN: ['1469-7750', '0024-6107']
DOI: https://doi.org/10.1112/jlms.12591