[Cohomologie et déformations des algèbres de Lie–Yamaguti de Rota–Baxter modifiées]
In this paper, first we introduce a notion of modified Rota–Baxter Lie–Yamaguti algebra of any weight. Also, we introduce the concept of a representation modified Rota–Baxter Lie–Yamaguti algebra of any weight. Then, we define a cohomology theory for modified Rota–Baxter Lie–Yamaguti algebras of any weight. As applications of the cohomology, we study formal deformations of modified Rota–Baxter Lie–Yamaguti algebras of arbitrary weights.
Dans cet article, nous introduisons d’abord la notion d’algèbre de Rota–Baxter Lie–Yamaguti modifiée de poids quelconque. Nous introduisons également le concept de représentation d’algèbre de Rota–Baxter Lie–Yamaguti modifiée de poids quelconque. Nous définissons ensuite une théorie de cohomologie pour les algèbres de Rota–Baxter Lie–Yamaguti modifiées de poids quelconque. Comme applications de la cohomologie, nous étudions les déformations formelles d’algèbres de Rota–Baxter Lie–Yamaguti modifiées de poids quelconque.
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Mots-clés : Algèbre de Lie–Yamaguti, opérateur de Rota–Baxter modifié, représentation, cohomologie, déformation
Khaled Basdouri 1 ; Sami Benabdelhafidh 1

@article{CRMATH_2025__363_G7_641_0, author = {Khaled Basdouri and Sami Benabdelhafidh}, title = {Cohomology and deformations of modified {Rota{\textendash}Baxter} {Lie{\textendash}Yamaguti} algebras}, journal = {Comptes Rendus. Math\'ematique}, pages = {641--662}, publisher = {Acad\'emie des sciences, Paris}, volume = {363}, year = {2025}, doi = {10.5802/crmath.743}, language = {en}, }
TY - JOUR AU - Khaled Basdouri AU - Sami Benabdelhafidh TI - Cohomology and deformations of modified Rota–Baxter Lie–Yamaguti algebras JO - Comptes Rendus. Mathématique PY - 2025 SP - 641 EP - 662 VL - 363 PB - Académie des sciences, Paris DO - 10.5802/crmath.743 LA - en ID - CRMATH_2025__363_G7_641_0 ER -
Khaled Basdouri; Sami Benabdelhafidh. Cohomology and deformations of modified Rota–Baxter Lie–Yamaguti algebras. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 641-662. doi : 10.5802/crmath.743. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.743/
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