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Radically filtered quasi-hereditary algebras and rigidity of tilting modules

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

HAZI, AMIT 

Abstract

jats:titleAbstract</jats:title>jats:pLetjats:italicA</jats:italic>be a quasi-hereditary algebra. We prove that in many cases, a tilting module is rigid (i.e. has identical radical and socle series) if it does not have certain subquotients whose composition factors extend more than one layer in the radical series or the socle series. We apply this theorem to show that the restricted tilting modules forjats:italicSL</jats:italic>jats:sub4</jats:sub>(jats:italicK</jats:italic>) are rigid, wherejats:italicK</jats:italic>is an algebraically closed field of characteristicjats:italicp</jats:italic>≥ 5.</jats:p>

Description

Keywords

4904 Pure Mathematics, 49 Mathematical Sciences

Journal Title

Mathematical Proceedings of the Cambridge Philosophical Society

Conference Name

Journal ISSN

0305-0041
1469-8064

Volume Title

163

Publisher

Cambridge University Press (CUP)