Veronese powers of operads and pure homotopy algebras
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00532206" target="_blank" >RIV/67985840:_____/20:00532206 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s40879-019-00351-6" target="_blank" >https://doi.org/10.1007/s40879-019-00351-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s40879-019-00351-6" target="_blank" >10.1007/s40879-019-00351-6</a>
Alternative languages
Result language
angličtina
Original language name
Veronese powers of operads and pure homotopy algebras
Original language description
We define the mth Veronese power of a weight graded operad [InlineEquation not available: see fulltext.] to be its suboperad [InlineEquation not available: see fulltext.] generated by operations of weight m. It turns out that, unlike Veronese powers of associative algebras, homological properties of operads are, in general, not improved by this construction. However, under some technical conditions, Veronese powers of quadratic Koszul operads are meaningful in the context of the Koszul duality theory. Indeed, we show that in many important cases the operads [InlineEquation not available: see fulltext.] are related by Koszul duality to operads describing strongly homotopy algebras with only one nontrivial operation. Our theory has immediate applications to objects such as Lie k-algebras and Lie triple systems. In the case of Lie k-algebras, we also discuss a similarly looking ungraded construction which is frequently used in the literature. We establish that the corresponding operad does not possess good homotopy properties, and that it leads to a very simple example of a non-Koszul quadratic operad for which the Ginzburg–Kapranov power series test is inconclusive.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA18-07776S" target="_blank" >GA18-07776S: Higher structures in algebra, geometry and mathematical physics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
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
European Journal of Mathematics
ISSN
2199-675X
e-ISSN
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Volume of the periodical
6
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
35
Pages from-to
829-863
UT code for WoS article
000569218800010
EID of the result in the Scopus database
2-s2.0-85068906275