Induced modules of support τ-tilting modules and extending modules of semibricks over blocks of finite groups

Ryotaro Koshio; Yuta Kozakai

doi:10.1016/j.jalgebra.2023.02.032

Induced modules of support τ-tilting modules and extending modules of semibricks over blocks of finite groups

Ryotaro Koshio, Yuta Kozakai

Department of Mathematics

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

6 Citations (Scopus)

Abstract

In this article we study support τ-tilting modules, semibricks and more over blocks of group algebras. Let k be an algebraically closed field of characteristic p>0, G˜ a finite group and G a normal subgroup of G˜. Moreover, let B˜ be a block of kG˜ and B a block of kG covered by B˜. We show that, under certain conditions for the factor group G˜/G and B, induced modules and extending modules of support τ-tilting modules and semibricks over B are also the ones over B˜, respectively.

Original language	English
Pages (from-to)	524-544
Number of pages	21
Journal	Journal of Algebra
Volume	628
DOIs	https://doi.org/10.1016/j.jalgebra.2023.02.032
Publication status	Published - 15 Aug 2023

Keywords

Blocks of finite groups
Semibricks
Support τ-tilting modules
Two-term simple-minded collections
Two-term tilting complexes

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10.1016/j.jalgebra.2023.02.032

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title = "Induced modules of support τ-tilting modules and extending modules of semibricks over blocks of finite groups",

abstract = "In this article we study support τ-tilting modules, semibricks and more over blocks of group algebras. Let k be an algebraically closed field of characteristic p>0, G˜ a finite group and G a normal subgroup of G˜. Moreover, let B˜ be a block of kG˜ and B a block of kG covered by B˜. We show that, under certain conditions for the factor group G˜/G and B, induced modules and extending modules of support τ-tilting modules and semibricks over B are also the ones over B˜, respectively.",

keywords = "Blocks of finite groups, Semibricks, Support τ-tilting modules, Two-term simple-minded collections, Two-term tilting complexes",

author = "Ryotaro Koshio and Yuta Kozakai",

note = "Funding Information: The authors are grateful to Naoko Kunugi for giving valuable comments. The first author would like to thank Yuta Katayama for useful advice about the group cohomology of the dihedral groups. Moreover, the authors are grateful to the anonymous referees for beneficial recommendations. Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",

year = "2023",

month = aug,

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doi = "10.1016/j.jalgebra.2023.02.032",

language = "English",

volume = "628",

pages = "524--544",

journal = "Journal of Algebra",

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T1 - Induced modules of support τ-tilting modules and extending modules of semibricks over blocks of finite groups

AU - Koshio, Ryotaro

AU - Kozakai, Yuta

N1 - Funding Information: The authors are grateful to Naoko Kunugi for giving valuable comments. The first author would like to thank Yuta Katayama for useful advice about the group cohomology of the dihedral groups. Moreover, the authors are grateful to the anonymous referees for beneficial recommendations. Publisher Copyright: © 2023 Elsevier Inc.

PY - 2023/8/15

Y1 - 2023/8/15

N2 - In this article we study support τ-tilting modules, semibricks and more over blocks of group algebras. Let k be an algebraically closed field of characteristic p>0, G˜ a finite group and G a normal subgroup of G˜. Moreover, let B˜ be a block of kG˜ and B a block of kG covered by B˜. We show that, under certain conditions for the factor group G˜/G and B, induced modules and extending modules of support τ-tilting modules and semibricks over B are also the ones over B˜, respectively.

AB - In this article we study support τ-tilting modules, semibricks and more over blocks of group algebras. Let k be an algebraically closed field of characteristic p>0, G˜ a finite group and G a normal subgroup of G˜. Moreover, let B˜ be a block of kG˜ and B a block of kG covered by B˜. We show that, under certain conditions for the factor group G˜/G and B, induced modules and extending modules of support τ-tilting modules and semibricks over B are also the ones over B˜, respectively.

KW - Blocks of finite groups

KW - Semibricks

KW - Support τ-tilting modules

KW - Two-term simple-minded collections

KW - Two-term tilting complexes

UR - http://www.scopus.com/inward/record.url?scp=85152411851&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2023.02.032

DO - 10.1016/j.jalgebra.2023.02.032

M3 - Article

AN - SCOPUS:85152411851

SN - 0021-8693

VL - 628

SP - 524

EP - 544

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Induced modules of support τ-tilting modules and extending modules of semibricks over blocks of finite groups

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Keywords

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