On Ideals and Derived and Central Descending Series of n-ary Hom-Algebras
2023 (English)In: Non-Associative Algebras and Related Topics: NAART II, Coimbra, Portugal, July 18–22, 2022 / [ed] Albuquerque, H., Brox, J., Martínez, C., Saraiva, P., Springer, 2023, Vol. 427, p. 261-286Conference paper, Published paper (Refereed)
Abstract [en]
The aim of this work is to explore some properties of n-ary skewsymmetric Hom-algebras and n-Hom-Lie algebras related to their ideals, derived series and central descending series. We extend the notions of derived series and central descending series to n-ary skew-symmetric Hom-algebras and provide various general conditions for their members to be Hom-subalgebras, weak ideals or Hom-ideals in the algebra or relatively to each other. In particular we study the invariance under the twisting maps of the derived series and central descending series and their subalgebra and ideal properties for a class of 3-dimensional Hom-Lie algebras and some 4-dimensional 3-Hom-Lie algebras. We also introduce a type of generalized ideals in n-ary Hom-algebras and present a few basic properties.
Place, publisher, year, edition, pages
Springer, 2023. Vol. 427, p. 261-286
Keywords [en]
Hom-algebra, n-Hom-Lie algebra, Derived series, Central descending series, Ideals
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-65193DOI: 10.1007/978-3-031-32707-0_17Scopus ID: 2-s2.0-85179628922ISBN: 9783031327063 (print)OAI: oai:DiVA.org:mdh-65193DiVA, id: diva2:1822124
Conference
2nd International Conference on Non-Associative Algebras and Related Topics, NAART II, Coimbra, Portugal, July 18–22, 2022
Funder
Sida - Swedish International Development Cooperation Agency2023-12-212023-12-212023-12-27Bibliographically approved