Quasi-Associative Algebras
| dc.contributor.author | Askar Dzhumadildaev | |
| dc.date.accessioned | 2025-11-04T06:31:57Z | |
| dc.date.available | 2025-11-04T06:31:57Z | |
| dc.date.issued | 2007 | |
| dc.description.abstract | This paper investigates a class of algebras obtained from associative algebras by introducing a q-commutator defined as a * b = ab + qba, where q belongs to a field K with characteristic not equal to 2 or 3, and q² is not equal to 0 or 1. Using this commutator, we construct algebras that form a variety characterized by a q-associativity identity. When the parameter satisfies q² − 4q + 1 ≠ 0, this identity alone describes the entire variety of q-associative algebras. However, when q² − 4q + 1 = 0, the q-associativity identity must be supplemented by the Lie-admissibility identity. In this exceptional case, the resulting variety is equivalent to the class of alternative algebras. Therefore, q-associative algebras form a structural link between associative, Lie-admissible, and alternative algebras, demonstrating how small changes in the commutator parameter q can transform fundamental algebraic properties. | |
| dc.identifier.citation | Askar Dzhumadildaev / Quasi-Associative Algebras / Suleyman Demirel University / Сду хабаршысы, 2007 | |
| dc.identifier.uri | https://repository.sdu.edu.kz/handle/123456789/2131 | |
| dc.language.iso | en | |
| dc.publisher | Suleyman Demirel University | |
| dc.rights | Attribution-NonCommercial-ShareAlike 4.0 International | en |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | |
| dc.subject | quasi-associative algebras | |
| dc.subject | q-commutator | |
| dc.subject | algebraic identities | |
| dc.subject | associators | |
| dc.subject | Lie-admissible algebras | |
| dc.subject | alternative algebras | |
| dc.title | Quasi-Associative Algebras | |
| dc.type | Article |