Representation Type and Stable Auslander-Reiten Components for Reduced Enveloping Algebras of Cartan Type

On Problem 8 of Benkart and Feldvoss: the representation type of the blocks of u_chi(g) for g a restricted simple Lie algebra of Cartan type, and the shapes of the stable Auslander-Reiten components. For terminal blocks with p >= 7 every nonperiodic stable component is one of ZA_infinity, ZA_infinity^infinity and ZD_infinity; the p = 7 terminal simple component is ZA_infinity, and complexity three forces the same for p >= 11. For r = p - 4 and p >= 7 the Euclidean stable components are excluded block-wide. On the rank-three canonical row strip the ambient-semisimple packet universe is reduced to four points.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-16
DOI
https://doi.org/10.5281/zenodo.22779569
Primary Topic
Algebraic structures and combinatorial models
Type
preprint
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preprint

Representation Type and Stable Auslander-Reiten Components for Reduced Enveloping Algebras of Cartan Type

CHAO MA
Zenodo (CERN European Organization for Nuclear Research)
Algebraic structures and combinatorial models
preprint

Representation Type and Stable Auslander-Reiten Components for Reduced Enveloping Algebras of Cartan Type

CHAO MA
preprint en

Abstract

On Problem 8 of Benkart and Feldvoss: the representation type of the blocks of u_chi(g) for g a restricted simple Lie algebra of Cartan type, and the shapes of the stable Auslander-Reiten components. For terminal blocks with p >= 7 every nonperiodic stable component is one of ZA_infinity, ZA_infinity^infinity and ZD_infinity; the p = 7 terminal simple component is ZA_infinity, and complexity three forces the same for p >= 11. For r = p - 4 and p >= 7 the Euclidean stable components are excluded block-wide. On the rank-three canonical row strip the ambient-semisimple packet universe is reduced to four points.

Zenodo (CERN European Organization for Nuclear Research)
Algebraic structures and combinatorial models
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