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Derivation problem for quandle algebras
Univ S Florida, Dept Math, Tampa, FL 33620 USA.
Univ Haute Alsace, IRIMAS Dept Math, 18 Rue Freres Lumiere, F-68093 Mulhouse, France.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0003-4554-6528
Univ Tartu, Inst Math & Stat, Narva Mnt 18, EE-51009 Tartu, Estonia.
2022 (English)In: International Journal of Algebra and Computation, ISSN 0218-1967, E-ISSN 1793-6500, Vol. 32, no 05, p. 985-1007Article in journal (Refereed) Published
Abstract [en]

The purpose of this paper is to introduce and investigate the notion of derivation for quandle algebras. More precisely, we describe the symmetries on structure constants providing a characterization for a linear map to be a derivation. We obtain a complete characterization of derivations in the case of quandle algebras of dihedral quandles over fields of characteristic zero, and provide the dimensionality of the Lie algebra of derivations. Many explicit examples and computations are given over both zero and positive characteristic. Furthermore, we investigate inner derivations, in the sense of Schafer for non-associative structures. We obtain necessary conditions for the Lie transformation algebra of quandle algebras of Alexander quandles, with explicit computations in low dimensions.

Place, publisher, year, edition, pages
2022. Vol. 32, no 05, p. 985-1007
Keywords [en]
Quandle, quandle algebra, derivation, Lie transformation algebra, dihedral quandle, Alexander quandle
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-59529DOI: 10.1142/S0218196722500424ISI: 000814097900006Scopus ID: 2-s2.0-85131099861OAI: oai:DiVA.org:mdh-59529DiVA, id: diva2:1681185
Available from: 2022-07-06 Created: 2022-07-06 Last updated: 2023-12-27Bibliographically approved

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Silvestrov, Sergei

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