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On the origin of higher braces and higher-order derivations
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SYSNO ASEP 0446764 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On the origin of higher braces and higher-order derivations Author(s) Markl, Martin (MU-W) RID, SAI, ORCID Source Title Journal of Homotopy and Related Structures - ISSN 2193-8407
Roč. 10, č. 3 (2015), s. 637-667Number of pages 31 s. Language eng - English Country GE - Georgia Keywords Koszul braces ; Börjeseon braces ; higher-order derivation Subject RIV BA - General Mathematics Institutional support MU-W - RVO:67985840 UT WOS 000360020800014 EID SCOPUS 84958523827 DOI 10.1007/s40062-014-0079-2 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2016
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