Cohomology and Ext for blocks whose Brauer trees are lines or stars

Jack Saunders

doi:10.1080/00927872.2024.2336134

Cohomology and Ext for blocks whose Brauer trees are lines or stars

Jack Saunders

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

We compute the dimensions of Ext𝑛𝐺⁢(𝑉,𝑊) for all irreducible modules V, W lying in r-blocks of cyclic defect whose Brauer tree is either a star or a line (open polygon), which in the line case extends a result of Dudas. We also make use of this information to aid in completing the same computation for all cross characteristic r-blocks of cyclic defect in rank one groups of Lie type.

Original language	English
Pages (from-to)	4059-4074
Number of pages	16
Journal	Communications in Algebra
Volume	52
Issue number	10
Early online date	23 Jul 2024
DOIs	https://doi.org/10.1080/00927872.2024.2336134
Publication status	Published - 2 Oct 2024

Bibliographical note

Publisher Copyright:
© 2024 The Author(s). Published with license by Taylor & Francis Group, LLC.

Access to Document

10.1080/00927872.2024.2336134Licence: CC BY-NC

Handle.net

Persistent link

Cite this

@article{abb02c3892374f2c92780a09e37e5419,

title = "Cohomology and Ext for blocks whose Brauer trees are lines or stars",

abstract = "We compute the dimensions of Ext𝑛𝐺⁢(𝑉,𝑊) for all irreducible modules V, W lying in r-blocks of cyclic defect whose Brauer tree is either a star or a line (open polygon), which in the line case extends a result of Dudas. We also make use of this information to aid in completing the same computation for all cross characteristic r-blocks of cyclic defect in rank one groups of Lie type.",

author = "Jack Saunders",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s). Published with license by Taylor & Francis Group, LLC.",

year = "2024",

month = oct,

day = "2",

doi = "10.1080/00927872.2024.2336134",

language = "English",

volume = "52",

pages = "4059--4074",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor & Francis Group",

number = "10",

}

TY - JOUR

T1 - Cohomology and Ext for blocks whose Brauer trees are lines or stars

AU - Saunders, Jack

PY - 2024/10/2

Y1 - 2024/10/2

N2 - We compute the dimensions of Ext𝑛𝐺⁢(𝑉,𝑊) for all irreducible modules V, W lying in r-blocks of cyclic defect whose Brauer tree is either a star or a line (open polygon), which in the line case extends a result of Dudas. We also make use of this information to aid in completing the same computation for all cross characteristic r-blocks of cyclic defect in rank one groups of Lie type.

AB - We compute the dimensions of Ext𝑛𝐺⁢(𝑉,𝑊) for all irreducible modules V, W lying in r-blocks of cyclic defect whose Brauer tree is either a star or a line (open polygon), which in the line case extends a result of Dudas. We also make use of this information to aid in completing the same computation for all cross characteristic r-blocks of cyclic defect in rank one groups of Lie type.

U2 - 10.1080/00927872.2024.2336134

DO - 10.1080/00927872.2024.2336134

M3 - Article (Academic Journal)

SN - 0092-7872

VL - 52

SP - 4059

EP - 4074

JO - Communications in Algebra

JF - Communications in Algebra

IS - 10

ER -

Cohomology and Ext for blocks whose Brauer trees are lines or stars

Abstract

Bibliographical note

Access to Document

Handle.net

Fingerprint

Cite this