Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2024, Early Access, 1 - 18
https://doi.org/10.24330/ieja.1580177

Öz

Kaynakça

  • G. Böhm, F. Nill and K. Szlachanyi, Weak Hopf algebras: I. Integral theory and $C^{*}$-structure, J. Algebra, 221(2) (1999), 385-438.
  • S. Caenepeel, F. Van Oystaeyen and Y. H. Zhang, Quantum Yang-Baxter module algebras, K-Theory, 8(3) (1994), 231-255.
  • J. F. Carinena, J. Grabowski and G. Marmo, Quantum bi-Hamiltonian systems, Internat. J. Modern Phys. A, 15(30) (2000), 4797-4810.
  • Y. Fang, H. H. Zheng and L. Y. Zhang, Modified Rota-Baxter paired modules and modified Rota-Baxter paired comodules, J. Shangdong Univ. Nat. Sci., 58(2) (2023), 93-104.
  • I. Z. Golubchik and V. V. Sokolov, Generalized operator Yang-Baxter equations, integrable ODEs and nonassociative algebras, J. Nonlinear Math. Phys., 7(2) (2000), 184-197.
  • I. Z. Golubchik and V. V. Sokolov, One more kind of the classical Yang-Baxter equation, Funct. Anal. Appl., 34(4) (2000), 296-298.
  • L. Guo, An Introduction to Rota-Baxter Algebra, Surveys of Modern Mathematics, 4, International Press, Somerville, MA; Higher Education Press, Beijing, 2012.
  • L. Guo, H. L. Lang and Y. H. Sheng, Integration and geometrization of Rota-Baxter Lie algebras, Adv. Math., 387 (2021), 107834 (34 pp).
  • L. Guo and Z. Z. Lin, Representations and modules of Rota-Baxter algebras, Asian J. Math., 25(6) (2021), 841-870.
  • R. Q. Jian, Construction of Rota-Baxter algebras via Hopf module algebras, Sci. China Math., 57 (2014), 2321-2328.
  • P. Lei and L. Guo, Nijenhuis algebras, NS algebras, and N-dendriform algebras, Front. Math. China, 7 (2012), 827-846.
  • P. Leroux, Construction of Nijenhuis operators and dendriform trialgebras, Int. J. Math. Math. Sci., 49 (2004), 2595-2615.
  • Z. H. Li and S. K. Wang, Rota-Baxter systems and skew trusses, J. Algebra, 623 (2023), 447-480.
  • F. Magri, A simple model of the integrable Hamiltonian equatio}, J. Math. Phys., 19(5) (1978), 1156-1162.
  • B. Mondal and R. Saha, Nijenhuis operators on Leibniz algebras, J. Geom. Phys., 196 (2024), 105057 (14 pp).
  • A. Nijenhuis, $\mathrm{X_{n-1}}$-Forming sets of eigenvectors, Indag. Math., 13 (1951), 200-212.
  • M. E. Sweedler, Hopf Algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969.
  • Q. Wang, Y. H. Sheng, C. M. Bai and J. F. Liu, Nijenhuis operators on pre-Lie algebras, Commun. Contemp. Math., 21(7) (2019), 1850050 (37 pp).
  • Y. Wang and L. Y. Zhang, The structure theorem and duality theorem for endomorphism algebras of weak Hopf algebras, J. Pure Appl. Algebra, 215(6) (2011), 1133-1145.
  • X. M. Wang, C. X. Zhang and L. Y. Zhang, Rota-Baxter operators on skew braces, Mathematics, 12(11) (2024), 1671 (14 pp).
  • L. Y. Zhang, Long bialgebras, dimodule algebras and quantum Yang-Baxter modules over Long bialgebras, Acta Math. Sin. (Engl. Ser.), 22(4) (2006), 1261-1270.
  • L. Y. Zhang, The structure theorem of weak comodule algebras}, Comm. Algebra, 38(1) (2010), 254-260.
  • L. Y. Zhang and W. T. Tong, Quantum Yang-Baxter $H$-module algebras and their braided products, Comm. Algebra, 31(5) (2003), 2471-2495.
  • H. H. Zheng, L. Guo and L. Y. Zhang, Rota-Baxter paired modules and their constructions from Hopf algebras, J. Algebra, 559 (2020), 601-624.

The deformation and construction of Nijenhuis paired modules

Yıl 2024, Early Access, 1 - 18
https://doi.org/10.24330/ieja.1580177

Öz

In this paper, we introduce the notion of Nijenhuis paired module, and give characterizations of Nijenhuis paired modules. Finally, we construct Nijenhuis paired modules from Hopf algebras, Hopf modules, dimodules and weak Hopf modules.

Kaynakça

  • G. Böhm, F. Nill and K. Szlachanyi, Weak Hopf algebras: I. Integral theory and $C^{*}$-structure, J. Algebra, 221(2) (1999), 385-438.
  • S. Caenepeel, F. Van Oystaeyen and Y. H. Zhang, Quantum Yang-Baxter module algebras, K-Theory, 8(3) (1994), 231-255.
  • J. F. Carinena, J. Grabowski and G. Marmo, Quantum bi-Hamiltonian systems, Internat. J. Modern Phys. A, 15(30) (2000), 4797-4810.
  • Y. Fang, H. H. Zheng and L. Y. Zhang, Modified Rota-Baxter paired modules and modified Rota-Baxter paired comodules, J. Shangdong Univ. Nat. Sci., 58(2) (2023), 93-104.
  • I. Z. Golubchik and V. V. Sokolov, Generalized operator Yang-Baxter equations, integrable ODEs and nonassociative algebras, J. Nonlinear Math. Phys., 7(2) (2000), 184-197.
  • I. Z. Golubchik and V. V. Sokolov, One more kind of the classical Yang-Baxter equation, Funct. Anal. Appl., 34(4) (2000), 296-298.
  • L. Guo, An Introduction to Rota-Baxter Algebra, Surveys of Modern Mathematics, 4, International Press, Somerville, MA; Higher Education Press, Beijing, 2012.
  • L. Guo, H. L. Lang and Y. H. Sheng, Integration and geometrization of Rota-Baxter Lie algebras, Adv. Math., 387 (2021), 107834 (34 pp).
  • L. Guo and Z. Z. Lin, Representations and modules of Rota-Baxter algebras, Asian J. Math., 25(6) (2021), 841-870.
  • R. Q. Jian, Construction of Rota-Baxter algebras via Hopf module algebras, Sci. China Math., 57 (2014), 2321-2328.
  • P. Lei and L. Guo, Nijenhuis algebras, NS algebras, and N-dendriform algebras, Front. Math. China, 7 (2012), 827-846.
  • P. Leroux, Construction of Nijenhuis operators and dendriform trialgebras, Int. J. Math. Math. Sci., 49 (2004), 2595-2615.
  • Z. H. Li and S. K. Wang, Rota-Baxter systems and skew trusses, J. Algebra, 623 (2023), 447-480.
  • F. Magri, A simple model of the integrable Hamiltonian equatio}, J. Math. Phys., 19(5) (1978), 1156-1162.
  • B. Mondal and R. Saha, Nijenhuis operators on Leibniz algebras, J. Geom. Phys., 196 (2024), 105057 (14 pp).
  • A. Nijenhuis, $\mathrm{X_{n-1}}$-Forming sets of eigenvectors, Indag. Math., 13 (1951), 200-212.
  • M. E. Sweedler, Hopf Algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969.
  • Q. Wang, Y. H. Sheng, C. M. Bai and J. F. Liu, Nijenhuis operators on pre-Lie algebras, Commun. Contemp. Math., 21(7) (2019), 1850050 (37 pp).
  • Y. Wang and L. Y. Zhang, The structure theorem and duality theorem for endomorphism algebras of weak Hopf algebras, J. Pure Appl. Algebra, 215(6) (2011), 1133-1145.
  • X. M. Wang, C. X. Zhang and L. Y. Zhang, Rota-Baxter operators on skew braces, Mathematics, 12(11) (2024), 1671 (14 pp).
  • L. Y. Zhang, Long bialgebras, dimodule algebras and quantum Yang-Baxter modules over Long bialgebras, Acta Math. Sin. (Engl. Ser.), 22(4) (2006), 1261-1270.
  • L. Y. Zhang, The structure theorem of weak comodule algebras}, Comm. Algebra, 38(1) (2010), 254-260.
  • L. Y. Zhang and W. T. Tong, Quantum Yang-Baxter $H$-module algebras and their braided products, Comm. Algebra, 31(5) (2003), 2471-2495.
  • H. H. Zheng, L. Guo and L. Y. Zhang, Rota-Baxter paired modules and their constructions from Hopf algebras, J. Algebra, 559 (2020), 601-624.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebir ve Sayı Teorisi
Bölüm Makaleler
Yazarlar

Yunfei Fang Bu kişi benim

Ximu Wang Bu kişi benim

Liangyun Zhang

Erken Görünüm Tarihi 6 Kasım 2024
Yayımlanma Tarihi
Gönderilme Tarihi 1 Haziran 2024
Kabul Tarihi 18 Eylül 2024
Yayımlandığı Sayı Yıl 2024 Early Access

Kaynak Göster

APA Fang, Y., Wang, X., & Zhang, L. (2024). The deformation and construction of Nijenhuis paired modules. International Electronic Journal of Algebra1-18. https://doi.org/10.24330/ieja.1580177
AMA Fang Y, Wang X, Zhang L. The deformation and construction of Nijenhuis paired modules. IEJA. Published online 01 Kasım 2024:1-18. doi:10.24330/ieja.1580177
Chicago Fang, Yunfei, Ximu Wang, ve Liangyun Zhang. “The Deformation and Construction of Nijenhuis Paired Modules”. International Electronic Journal of Algebra, Kasım (Kasım 2024), 1-18. https://doi.org/10.24330/ieja.1580177.
EndNote Fang Y, Wang X, Zhang L (01 Kasım 2024) The deformation and construction of Nijenhuis paired modules. International Electronic Journal of Algebra 1–18.
IEEE Y. Fang, X. Wang, ve L. Zhang, “The deformation and construction of Nijenhuis paired modules”, IEJA, ss. 1–18, Kasım 2024, doi: 10.24330/ieja.1580177.
ISNAD Fang, Yunfei vd. “The Deformation and Construction of Nijenhuis Paired Modules”. International Electronic Journal of Algebra. Kasım 2024. 1-18. https://doi.org/10.24330/ieja.1580177.
JAMA Fang Y, Wang X, Zhang L. The deformation and construction of Nijenhuis paired modules. IEJA. 2024;:1–18.
MLA Fang, Yunfei vd. “The Deformation and Construction of Nijenhuis Paired Modules”. International Electronic Journal of Algebra, 2024, ss. 1-18, doi:10.24330/ieja.1580177.
Vancouver Fang Y, Wang X, Zhang L. The deformation and construction of Nijenhuis paired modules. IEJA. 2024:1-18.