Pure Projective Tilting Modules

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10420934" target="_blank" >RIV/00216208:11320/20:10420934 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=7muzym7uqj" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=7muzym7uqj</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-43416-8" target="_blank" >10.1007/978-3-030-43416-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Pure Projective Tilting Modules

Popis výsledku v původním jazyce

Let TR be a 1-tilting module with tilting torsion pair (Gen T,F) in Mod-R. The following conditions are proved to be equivalent: (1) T is pure projective; (2) Gen T is a definable subcategory of Mod-R with enough pure projectives; (3) both classes Gen T and F are finitely axiomatizable; and (4) the heart of the corresponding HRS t-structure (in the derived category Db(Mod-R)) is Grothendieck. This article explores in this context the question raised by Saor&apos;ın if the Grothendieck condition on the heart of an HRS t-structure implies that it is equivalent to a module category. This amounts to asking if T is tilting equivalent to a finitely presented module. This is resolved in the positive for a Krull-Schmidt ring, and for a commutative ring, a positive answer follows from a proof that every pure projective 1-tilting module is projective. However, a general criterion is found that yields a negative answer to Saor&apos;ın&apos;s Question and this criterion is satisfied by the universal enveloping algebra of a semisimple Lie algebra, a left and right noetherian domain.

Název v anglickém jazyce

Pure Projective Tilting Modules

Popis výsledku anglicky

Let TR be a 1-tilting module with tilting torsion pair (Gen T,F) in Mod-R. The following conditions are proved to be equivalent: (1) T is pure projective; (2) Gen T is a definable subcategory of Mod-R with enough pure projectives; (3) both classes Gen T and F are finitely axiomatizable; and (4) the heart of the corresponding HRS t-structure (in the derived category Db(Mod-R)) is Grothendieck. This article explores in this context the question raised by Saor&apos;ın if the Grothendieck condition on the heart of an HRS t-structure implies that it is equivalent to a module category. This amounts to asking if T is tilting equivalent to a finitely presented module. This is resolved in the positive for a Krull-Schmidt ring, and for a commutative ring, a positive answer follows from a proof that every pure projective 1-tilting module is projective. However, a general criterion is found that yields a negative answer to Saor&apos;ın&apos;s Question and this criterion is satisfied by the universal enveloping algebra of a semisimple Lie algebra, a left and right noetherian domain.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA14-15479S" target="_blank" >GA14-15479S: Teorie reprezentací (strukturní rozklady a jejich meze)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Documenta Mathematica

ISSN

1431-0635

e-ISSN

—

Svazek periodika

2020

Číslo periodika v rámci svazku

25

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

24

Strana od-do

401-424

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85092911851