2000 character limit reached
Compatible Associative Algebras and Some Invariants (2405.18243v2)
Published 28 May 2024 in math.RA
Abstract: A compatible associative algebra is a vector space equipped with two associative multiplication structures that interact in a certain natural way. This article presents the classification of these algebras with dimension less than four, as well as the classifications of their corresponding derivations, centroids, automorphisms, and quasi-centroids. We then characterize a selection of further invariants such as Rota-Baxter operators and second cohomology for some specific examples.
- Alkhezi, Y.A.; Fiidow, M.A. “Inner Derivations of Finite Dimensional Dendriform Algebras.” International Mathematical Forum, Vol. 17, No. 4 (2022).
- Arfa, A.; Saadaoui, N.; Silvestrov, S. “Classification, Centroids and Derivations of Two-Dimensional Hom-Leibniz Algebras” in Non-commutative and Non-associative Algebra and Analysis Structures, SPAS 2019. Springer Proceedings in Mathematics & Statistics, Vol 426 (2023). Springer Cham.
- Basri, W. “Classification and derivations of low-dimensional complex dialgebras” (2014). Doctoral thesis, Universiti Putra Malaysia.
- Basri, W.; Rakhimov, I. S.; Rikhsiboev, I. M. “Complete lists of low dimensional complex associative algebras” (2009). arXiv:0910.0932.
- Chtioui, T; Das, A.; Mabrouk, S. “(Co)homology of compatible associative algebras.” Communications in Algebra, Vol. 52, No. 2 (2024).
- Fiidow, M.A.; Rakhimov, I.S.; Said Husain, S.K. “Centroids and Derivations of Associative Algebras.” Proceedings of the IEEE (2015).
- Leger, G.F.; Luks, E.M. “Generalized Derivations of Lie Algebras.” Journal of Algebra, Vol. 228, No. 1 (2000).
- Mainellis, E. “Multipliers and covers of perfect diassociative algebras.” Journal of Algebra and Its Applications (2023). https://doi.org/10.1142/S021949882450244X
- Mainellis, E. “Multipliers and Unicentral Diassociative Algebras.” Journal of Algebra and Its Applications, Vol. 22, No. 05 (2023).
- Mainellis, E. “Multipliers of Nilpotent Diassociative Algebras.” Results in Mathematics, Vol. 77, No. 191 (2022).
- Makhlouf, A.; Zahari, A. “Structure and Classification of Hom-Associative Algebras.” Acta et commentationes universitis Tartuensis de mathematica, Vol. 24, No. 1 (2020).
- Mazzola, G. “The algebraic and geometric classification of associative algebras of dimension five.” manuscripta mathematica, Vol. 27 (1979).
- Mosbahi, B.; Basdouri, I.; Zahari, A. “Classification, α𝛼\alphaitalic_α-Inner Derivations and α𝛼\alphaitalic_α-Centroids of Finite-Dimensional Complex Hom-Trialgebras.” Pure and Applied Mathematics Journal, Vol. 12, No. 5 (2023).
- Su, Y.; Xu, X.; Zhang, H. “Derivation-simple algebras and the structures of Lie algebras of Witt type.” Journal of Algebra, Vol. 233, No. 2 (2000).
- Zahari, A.; Bakayoko, I. “On BiHom-Associative dialgebras.” Open Journal of Mathematical Sciences, Vol. 7, No. 1 (2023).
Sponsor
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.