Calculus of multilinear differential operators, operator L∞-algebras and IBL∞-algebras
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Calculus of multilinear differential operators, operator L∞-algebras and IBL∞-algebras
Original language description
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.
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
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Geometry and Physics
ISSN
0393-0440
e-ISSN
1879-1662
Volume of the periodical
173
Issue of the periodical within the volume
March
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
40
Pages from-to
104431
UT code for WoS article
000791034100010
EID of the result in the Scopus database
2-s2.0-85120815433