Calculus of multilinear differential operators, operator L∞-algebras and IBL∞-algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00549804" target="_blank" >RIV/67985840:_____/22:00549804 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.geomphys.2021.104431" target="_blank" >https://doi.org/10.1016/j.geomphys.2021.104431</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.geomphys.2021.104431" target="_blank" >10.1016/j.geomphys.2021.104431</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Calculus of multilinear differential operators, operator L∞-algebras and IBL∞-algebras

Popis výsledku v původním jazyce

We propose an operadic framework suitable for describing algebraic structures with operations being multilinear differential operators of varying orders or, more generally, formal series of such operators. The framework is built upon the notion of a multifiltration of a linear operad generalizing the concept of a filtration of an associative algebra. We describe a particular way of constructing and analyzing multifiltrations based on a presentation of a linear operad in terms of generators and relations. In particular, that allows us to observe a special role played in this context by Lie, Lie-admissible and Lie∞-structures. As a main application, and the original motivation for the present work, we show how a certain generalization of the well-known big bracket construction of Lecomte–Roger and Kosmann-Schwarzbach encompassing the case of homotopy involutive Lie bialgebras can be obtained.

Název v anglickém jazyce

Calculus of multilinear differential operators, operator L∞-algebras and IBL∞-algebras

Popis výsledku anglicky

We propose an operadic framework suitable for describing algebraic structures with operations being multilinear differential operators of varying orders or, more generally, formal series of such operators. The framework is built upon the notion of a multifiltration of a linear operad generalizing the concept of a filtration of an associative algebra. We describe a particular way of constructing and analyzing multifiltrations based on a presentation of a linear operad in terms of generators and relations. In particular, that allows us to observe a special role played in this context by Lie, Lie-admissible and Lie∞-structures. As a main application, and the original motivation for the present work, we show how a certain generalization of the well-known big bracket construction of Lecomte–Roger and Kosmann-Schwarzbach encompassing the case of homotopy involutive Lie bialgebras can be obtained.

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

2022

Kód důvěrnosti údajů

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

Název periodika

Journal of Geometry and Physics

ISSN

0393-0440

e-ISSN

1879-1662

Svazek periodika

173

Číslo periodika v rámci svazku

March

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

40

Strana od-do

104431

Kód UT WoS článku

000791034100010

EID výsledku v databázi Scopus

2-s2.0-85120815433