On the vertices of indecomposable modules over dihedral 2-groups

Guodong Zhou

doi:10.1016/j.jalgebra.2009.01.005

On the vertices of indecomposable modules over dihedral 2-groups

Guodong Zhou

Université de Picardie Jules Verne

Research output: Contribution to journal › Article › peer-review

Abstract

Let k be an algebraically closed field of characteristic 2. We calculate the vertices of all indecomposable k D₈-modules for the dihedral group D₈ of order 8. We also give a conjectural formula of the induced module of a string module from k T₀ to kG where G is a dihedral group of order ≥8 and where T₀ is a dihedral subgroup of index 2 of G. Some cases where we verified this formula are given.

Original language	English
Pages (from-to)	1661-1685
Number of pages	25
Journal	Journal of Algebra
Volume	321
Issue number	6
DOIs	https://doi.org/10.1016/j.jalgebra.2009.01.005
State	Published - 15 Mar 2009
Externally published	Yes

Keywords

Band module
Dihedral group
String module
Vertex

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10.1016/j.jalgebra.2009.01.005

Cite this

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title = "On the vertices of indecomposable modules over dihedral 2-groups",

abstract = "Let k be an algebraically closed field of characteristic 2. We calculate the vertices of all indecomposable k D8-modules for the dihedral group D8 of order 8. We also give a conjectural formula of the induced module of a string module from k T0 to kG where G is a dihedral group of order ≥8 and where T0 is a dihedral subgroup of index 2 of G. Some cases where we verified this formula are given.",

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N2 - Let k be an algebraically closed field of characteristic 2. We calculate the vertices of all indecomposable k D8-modules for the dihedral group D8 of order 8. We also give a conjectural formula of the induced module of a string module from k T0 to kG where G is a dihedral group of order ≥8 and where T0 is a dihedral subgroup of index 2 of G. Some cases where we verified this formula are given.

AB - Let k be an algebraically closed field of characteristic 2. We calculate the vertices of all indecomposable k D8-modules for the dihedral group D8 of order 8. We also give a conjectural formula of the induced module of a string module from k T0 to kG where G is a dihedral group of order ≥8 and where T0 is a dihedral subgroup of index 2 of G. Some cases where we verified this formula are given.

KW - Band module

KW - Dihedral group

KW - String module

KW - Vertex

UR - https://www.scopus.com/pages/publications/58749104510

U2 - 10.1016/j.jalgebra.2009.01.005

DO - 10.1016/j.jalgebra.2009.01.005

M3 - 文章

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SN - 0021-8693

VL - 321

SP - 1661

EP - 1685

JO - Journal of Algebra

JF - Journal of Algebra

IS - 6

ER -

On the vertices of indecomposable modules over dihedral 2-groups

Abstract

Keywords

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