The Jordan-Hölder property and Grothendieck monoids of exact categories
Published in Adv. Math., February 2022. Links: journal, arXiv:1908.05446
Citation: H. Enomoto, The Jordan-Hölder property and Grothendieck monoids of exact categories, Adv. Math. 396 (2022), Paper No. 108167.
Comment
I consider when an exact category satisfies the Jordan-Hölder property, (JHP) (the uniqueness of decompositions of object into simple objects). I gave a characterization of it by using an invariant “Grothendieck monoid” of exact categories In many cases arising in the rep. theory of algebras, (JHP) is equivalent to “number of projectives = number of simples”. I investigated simples in torsion-free classes over type A quiver by using the symmetric group, and observed that Bruhat order appears!
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