Veronese powers of operads and pure homotopy algebras

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Veronese powers of operads and pure homotopy algebras

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Veronese powers of operads and pure homotopy algebras

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-07776S" target="_blank" >GA18-07776S: Vyšší struktury v algebře, geometrii a matematické fyzice</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

European Journal of Mathematics

ISSN

2199-675X

e-ISSN

—

Svazek periodika

6

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

35

Strana od-do

829-863

Kód UT WoS článku

000569218800010

EID výsledku v databázi Scopus

2-s2.0-85068906275