Pure Projective Tilting Modules
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Pure Projective Tilting Modules
Original language description
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'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'ın's Question and this criterion is satisfied by the universal enveloping algebra of a semisimple Lie algebra, a left and right noetherian domain.
Czech name
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA14-15479S" target="_blank" >GA14-15479S: Representation Theory (Structural Decompositions and Their Constraints)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Documenta Mathematica
ISSN
1431-0635
e-ISSN
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Volume of the periodical
2020
Issue of the periodical within the volume
25
Country of publishing house
DE - GERMANY
Number of pages
24
Pages from-to
401-424
UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-85092911851