Lifting Brauer-friendly modules

Nobukatsu Watanabe

doi:10.55937/sut/1610061557

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Home > Journals > SUT J. Math. > Volume 56 > Issue 2 > Article

December 2020 Lifting Brauer-friendly modules

Nobukatsu Watanabe

Author Affiliations +

Nobukatsu Watanabe¹
¹Department of Mathematics, Tokyo University of Science Kagurazaka 1–3, Shinjuku, Tokyo 162–8601, Japan

SUT J. Math. 56(2): 171-177 (December 2020). DOI: 10.55937/sut/1610061557

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Abstract

Let ${\cal O}$ be a complete discrete valuation ring with a residue field $k = {\cal O}/J({\cal O})$ of characteristic $p$ , $G$ a finite group, and $b$ a block of $k G$ with lift $\hat b$ . In this paper, we show that any indecomposable Brauer-friendly $k G b$ -module satisfying certain condition is liftable to an indecomposable Brauer-friendly ${\cal O}G\hat b$ -module.

Acknowledgement

The author would like to thank Naoko Kunugi for her careful reading and useful comments in an earlier version of the paper. The author also would like to thank the referee for her or his useful comments.