The general operadic approach to splitting algebraic operations was developed in [1]. By splitting the product in a given algebraic variety $\mathcal{C}$, notion of $\mathcal{C}$-dendriform algebras was systematically studied in[2]. This article aims to study ``anti-associative dendriform algebras", which offer an approach to addressing anti-associativity. These algebras are defined by two operations whose sum is anti-associative. Furthermore, the notion of $\mathcal{O}$-operators on anti-associative algebras is presented as a tool to interpret anti-associative dendriform algebras. Moreover, anti-associative algebras with nondegenerate Connes cocycles admit compatible anti-associative dendriform algebra structures.
| Mualliflar | Normatov, Zafar |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2026-07-02 |
| Jild | 70 |
| Son | 2 |
| Betlar | 174-186 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2026-2-21 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2026-2-21 · Maqolaning asl sahifasi
Lie algebra, pre-Lie algebra, dendriform algebra, Jacobi-Jordan algebra, pre-Jacobi-Jordan algebra, $\mathcal O$-operator
| APA | Normatov, Zafar (2026). Anti-associative dendriform algebras. O‘zbekiston matematika jurnali, 70(2), 174-186. https://doi.org/10.29229/uzmj.2026-2-21 |
|---|---|
| GOST (OAK) | Normatov, Zafar Anti-associative dendriform algebras // O‘zbekiston matematika jurnali. – 2026. – T. 70, № 2. – P. 174-186. – DOI: 10.29229/uzmj.2026-2-21. |
| MLA | Normatov, Zafar. “Anti-associative dendriform algebras.” O‘zbekiston matematika jurnali, 70(2), 174-186, 2026. https://doi.org/10.29229/uzmj.2026-2-21 |
| Chicago | Normatov, Zafar. “Anti-associative dendriform algebras.” O‘zbekiston matematika jurnali, 70(2), 174-186 (2026). https://doi.org/10.29229/uzmj.2026-2-21 |
| Harvard | Normatov, Zafar (2026) ‘Anti-associative dendriform algebras’, O‘zbekiston matematika jurnali, 70(2), 174-186. https://doi.org/10.29229/uzmj.2026-2-21 |
| BibTeX | @article{normatovzafar2026,
title = {Anti-associative dendriform algebras},
author = {Normatov, Zafar},
journal = {O‘zbekiston matematika jurnali},
year = {2026},
volume = {70},
number = {2},
pages = {174-186},
doi = {10.29229/uzmj.2026-2-21},
url = {https://doi.org/10.29229/uzmj.2026-2-21}
} |
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