Derivations and biderivations in dialgebras
The concepts of derivations and antiderivations for Leibniz algebras naturally arise from the inner operators determined by their algebraic structure. In this paper, we introduce the corresponding analogues in the setting of dialgebras, which we call diderivations, and examine their structural prope...
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| Datum: | 2026 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2026
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2457 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1861680840594948096 |
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| author | Restrepo-Sánchez, Gabriel Gustavo Rodríguez-Nieto, José Gregorio Salazar-Díaz, Olga Patricia Sarrazola-Alzate, Andrés Velásquez, Raúl |
| author_facet | Restrepo-Sánchez, Gabriel Gustavo Rodríguez-Nieto, José Gregorio Salazar-Díaz, Olga Patricia Sarrazola-Alzate, Andrés Velásquez, Raúl |
| author_sort | Restrepo-Sánchez, Gabriel Gustavo |
| baseUrl_str | https://admjournal.luguniv.edu.ua/index.php/adm/oai |
| collection | OJS |
| datestamp_date | 2026-04-05T09:02:49Z |
| description | The concepts of derivations and antiderivations for Leibniz algebras naturally arise from the inner operators determined by their algebraic structure. In this paper, we introduce the corresponding analogues in the setting of dialgebras, which we call diderivations, and examine their structural properties in relation to classical derivations and multiplicative operators. Our approach is based on the study of left and right multiplication operators and on the construction of the Leibniz algebra generated by biderivations, thereby providing a systematic operator-theoretic framework that unifies several derivation-like structures. In addition to the general theory, we present a complete classification of the spaces of diderivations for dialgebras of dimensions two and three, obtained through explicit computations. These low-dimensional results not only illustrate the general constructions but also reveal structural patterns that inform possible extensions to higher dimensions and more intricate algebraic contexts. |
| doi_str_mv | 10.12958/adm2457 |
| first_indexed | 2026-04-06T01:00:02Z |
| format | Article |
| id | admjournalluguniveduua-article-2457 |
| institution | Algebra and Discrete Mathematics |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-04-06T01:00:02Z |
| publishDate | 2026 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-24572026-04-05T09:02:49Z Derivations and biderivations in dialgebras Restrepo-Sánchez, Gabriel Gustavo Rodríguez-Nieto, José Gregorio Salazar-Díaz, Olga Patricia Sarrazola-Alzate, Andrés Velásquez, Raúl dialgebras, derivations, diderivations, Leibniz algebras, algebraic classification 17A32, 17A36 The concepts of derivations and antiderivations for Leibniz algebras naturally arise from the inner operators determined by their algebraic structure. In this paper, we introduce the corresponding analogues in the setting of dialgebras, which we call diderivations, and examine their structural properties in relation to classical derivations and multiplicative operators. Our approach is based on the study of left and right multiplication operators and on the construction of the Leibniz algebra generated by biderivations, thereby providing a systematic operator-theoretic framework that unifies several derivation-like structures. In addition to the general theory, we present a complete classification of the spaces of diderivations for dialgebras of dimensions two and three, obtained through explicit computations. These low-dimensional results not only illustrate the general constructions but also reveal structural patterns that inform possible extensions to higher dimensions and more intricate algebraic contexts. Lugansk National Taras Shevchenko University 2026-04-05 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2457 10.12958/adm2457 Algebra and Discrete Mathematics; Vol 41, No 1 (2026) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2457/pdf Copyright (c) 2026 Algebra and Discrete Mathematics |
| spellingShingle | dialgebras derivations diderivations Leibniz algebras algebraic classification 17A32 17A36 Restrepo-Sánchez, Gabriel Gustavo Rodríguez-Nieto, José Gregorio Salazar-Díaz, Olga Patricia Sarrazola-Alzate, Andrés Velásquez, Raúl Derivations and biderivations in dialgebras |
| title | Derivations and biderivations in dialgebras |
| title_full | Derivations and biderivations in dialgebras |
| title_fullStr | Derivations and biderivations in dialgebras |
| title_full_unstemmed | Derivations and biderivations in dialgebras |
| title_short | Derivations and biderivations in dialgebras |
| title_sort | derivations and biderivations in dialgebras |
| topic | dialgebras derivations diderivations Leibniz algebras algebraic classification 17A32 17A36 |
| topic_facet | dialgebras derivations diderivations Leibniz algebras algebraic classification 17A32 17A36 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2457 |
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