On the origin of higher braces and higher-order derivations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F15%3A00446764" target="_blank" >RIV/67985840:_____/15:00446764 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/15:10335212
Result on the web
<a href="http://dx.doi.org/10.1007/s40062-014-0079-2" target="_blank" >http://dx.doi.org/10.1007/s40062-014-0079-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s40062-014-0079-2" target="_blank" >10.1007/s40062-014-0079-2</a>
Alternative languages
Result language
angličtina
Original language name
On the origin of higher braces and higher-order derivations
Original language description
The classical Koszul braces, sometimes also called the Koszul hierarchy, were introduced in 1985 by Koszul (Astérisque, (Numero Hors Serie):257?271, 1985). Their non-commutative counterparts came as a surprise much later, in 2013, in a preprint by Börjeson (... -algebras derived from associative algebras with a non-derivation differential, Preprint arXiv:1304.6231, 2013). In Part I we show that both braces are the twistings of the trivial ... (resp. ...) algebra by a specific automorphism of the underlying coalgebra. This gives an astonishingly simple proof of their properties. Using the twisting, we construct other surprising examples of ... and ... braces. We finish Part 1 by discussing ... braces related to Lie algebras. In Part 2 we prove that in fact all natural braces are the twistings by unique automorphisms. We also show that there is precisely one hierarchy of braces that leads to a sensible notion of higher-order derivations.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
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 Homotopy and Related Structures
ISSN
2193-8407
e-ISSN
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Volume of the periodical
10
Issue of the periodical within the volume
3
Country of publishing house
GE - GEORGIA
Number of pages
31
Pages from-to
637-667
UT code for WoS article
000360020800014
EID of the result in the Scopus database
2-s2.0-84958523827