Indecomposable Jordan types of Loewy length 2

Let k be an algebraically closed field, char(k)=p≥2 and Er be a elementary abelian p-group of rank r≥2. Let (c,d)∈N2. We show that there exists an indecomposable module of constant Jordan type [1]c[2]d and Loewy length 2 if and only if qΓr(d,d+c)≤1 and c≥r−1, where qΓr(x,y):=x2+y2−rxy denotes the Ti...

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Bibliographic Details
Published in:Journal of algebra 2020-08, Vol.556, p.67-92
Main Author: Bissinger, Daniel
Format: Article
Language:English
Subjects:
Constant Jordan type
Covering theory
Kronecker algebra
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Summary:Let k be an algebraically closed field, char(k)=p≥2 and Er be a elementary abelian p-group of rank r≥2. Let (c,d)∈N2. We show that there exists an indecomposable module of constant Jordan type [1]c[2]d and Loewy length 2 if and only if qΓr(d,d+c)≤1 and c≥r−1, where qΓr(x,y):=x2+y2−rxy denotes the Tits form of the generalized Kronecker quiver Γr. Since p>2 and constant Jordan type [1]c[2]d imply Loewy length ≤2, we get in this case the full classification of Jordan types [1]c[2]d that arise from indecomposable modules.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2020.03.010