Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, , 12 - 34, 08.01.2019
https://doi.org/10.24330/ieja.504101

Öz

Kaynakça

  • M. Aguiar, On the associative analog of Lie bialgebras, J. Algebra, 244(2) (2001), 492-532.
  • F. V.Atkinson, Some aspects of Baxter's functional equation, J. Math. Anal. Appl., 7 (1963), 1-30.
  • C. Bai, O. Bellier, L. Guo and X. Ni, Splitting of operations, Manin products, and Rota-Baxter operators, Int. Math. Res. Not. IMRN, (2013) 3 (2013), 485- 524.
  • C. Bai, L. Guo and X. Ni, Nonabelian generalized Lax pairs, the classical Yang- Baxter equation and PostLie algebras, Comm. Math. Phys., 297(2) (2010), 553-596.
  • C. Bai, L. Guo and X. Ni, Generalizations of the classical Yang-Baxter equation and O-operators, J. Math. Phys., 52(6) (2011), 063515 (17 pp).
  • C. Bai, L. Guo and X. Ni, O-operators on associative algebras and associative Yang-Baxter equations, Paci c J. Math., 256(2) (2012), 257-289.
  • C. Bai, L. Guo and X. Ni, O-operators on associative algebras, associative Yang-Baxter equations and dendriform algebras, In \Quantized Algebra and Physics", Nankai Ser. Pure Appl. Math. Theoret. Phys., 8, World Sci. Publ., Hackensack, NJ, (2012), 10-51.
  • G. Baxter, An analytic problem whose solution follows from a simple algebraic identity, Paci c J. Math., 10 (1960), 731-742.
  • M. Bordemann, Generalized Lax pairs, the modi ed classical Yang-Baxter equa- tion, and ane geometry of Lie groups, Comm. Math. Phys., 135(1) (1990), 201-216.
  • P. Cartier, On the structure of free Baxter algebras, Advances in Math., 9 (1972), 253-265.
  • A. Connes and D. Kreimer, Hopf algebras, renormalization and noncommuta- tive geometry, Comm. Math. Phys., 199(1) (1998), 203-242.
  • K. Ebrihimi-Fard, Loday-type algebras and the Rota-Baxter relation, Lett. Math. Phys., 61(2) (2002), 139-147.
  • K. Ebrahimi-Fard and L. Guo, Quasi-shues, mixable shues and Hopf alge- bras, J. Algebraic Combin., 24(1) (2006), 83-101.
  • K. Ebrahimi-Fard and L. Guo, Rota-Baxter algebras and dendriform algebras, J. Pure Appl. Algebra, 212(2) (2008), 320-339.
  • X. Gao, L. Guo and T. Zhang, Bialgebra and Hopf algebra structures on free Rota-Baxter algebra, arXiv:1604.03238.
  • L. Guo, An Introduction to Rota-Baxter Algebra, Surveys of Modern Mathematics, 4, International Press, Somerville, MA; Higher Education Press, Beijing, 2012.
  • L. Guo and W. Keigher, Baxter algebras and shue products, Adv. Math., 150(1) (2000), 117-149.
  • L. Guo and W. Y. Sit Enumeration and generating functions of Rota-Baxter words, Math. Comput. Sci., 4(2-3) (2010), 313-337.
  • R. Jian and J. Zhang, Rota-Baxter coalgebras, arXiv:1409.3052. [20] Y. Kosmann-Schwarzbach, Lie bialgebras, Poisson Lie groups and dressing transformations, in \Integrability of nonlinear systems", Lecture Notes in Phys., 495, Springer, Berlin, (1997), 104-170.
  • T. Ma and L. Liu, Rota-Baxter coalgebras and Rota-Baxter bialgebras, Linear Multilinear Algebra, 64(5) (2016), 968-979.
  • A. Makhlouf and D. Yau, Rota-Baxter Hom-Lie-admissible algebras, Comm. Algebra, 42(3) (2014), 1231-1257.
  • D. Manchon, Hoft algebras, from basics to applications to renormalization, Comptes-rendus des Rencontres mathematiques de Glanon, 2001.
  • M. Marcolli and X. Ni, Rota-Baxter algebras, singular hypersurfaces, and renormalization on Kausz compacti cations, J. Singul., 15 (2016), 80-117.
  • J. Pei, C. Bai and L. Guo, Splitting of operads and Rota-Baxter operators on operads, Appl. Categ. Structures, 25(4) (2017), 505-538.
  • G.-C. Rota, Baxter algebras and combinatorial identities I, II, Bull. Amer. Math. Soc., 75 (1969), 325-329, 330-334.
  • M. A. Semenov-Tian-Shansky, What is a classical R-matrix? Functional Anal. Appl. 17(4) (1983), 259-272.
  • T. Zhang, X. Gao and L. Guo, Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras, J. Math. Phys., 57(10) (2016), 101701 (16 pp).
  • X. Zhang, X. Gao and L. Guo, Commutative modi ed Rota-Baxter algebras, shuffe products and Hopf algebras, Bull. Malays. Math. Sci. Soc., (2018), https://doi.org/10.1007/s40840-018-0648-3.

FREE MODIFIED ROTA-BAXTER ALGEBRAS AND HOPF ALGEBRAS

Yıl 2019, , 12 - 34, 08.01.2019
https://doi.org/10.24330/ieja.504101

Öz

The notion of a modi ed Rota-Baxter algebra comes from the
combination of those of a Rota-Baxter algebra and a modi ed Yang-Baxter
equation. In this paper, we rst construct free modi ed Rota-Baxter algebras.
We then equip a free modi ed Rota-Baxter algebra with a bialgebra structure
by a cocycle construction. Under the assumption that the generating algebra
is a connected bialgebra, we further equip the free modi ed Rota-Baxter alge-
bra with a Hopf algebra structure.

Kaynakça

  • M. Aguiar, On the associative analog of Lie bialgebras, J. Algebra, 244(2) (2001), 492-532.
  • F. V.Atkinson, Some aspects of Baxter's functional equation, J. Math. Anal. Appl., 7 (1963), 1-30.
  • C. Bai, O. Bellier, L. Guo and X. Ni, Splitting of operations, Manin products, and Rota-Baxter operators, Int. Math. Res. Not. IMRN, (2013) 3 (2013), 485- 524.
  • C. Bai, L. Guo and X. Ni, Nonabelian generalized Lax pairs, the classical Yang- Baxter equation and PostLie algebras, Comm. Math. Phys., 297(2) (2010), 553-596.
  • C. Bai, L. Guo and X. Ni, Generalizations of the classical Yang-Baxter equation and O-operators, J. Math. Phys., 52(6) (2011), 063515 (17 pp).
  • C. Bai, L. Guo and X. Ni, O-operators on associative algebras and associative Yang-Baxter equations, Paci c J. Math., 256(2) (2012), 257-289.
  • C. Bai, L. Guo and X. Ni, O-operators on associative algebras, associative Yang-Baxter equations and dendriform algebras, In \Quantized Algebra and Physics", Nankai Ser. Pure Appl. Math. Theoret. Phys., 8, World Sci. Publ., Hackensack, NJ, (2012), 10-51.
  • G. Baxter, An analytic problem whose solution follows from a simple algebraic identity, Paci c J. Math., 10 (1960), 731-742.
  • M. Bordemann, Generalized Lax pairs, the modi ed classical Yang-Baxter equa- tion, and ane geometry of Lie groups, Comm. Math. Phys., 135(1) (1990), 201-216.
  • P. Cartier, On the structure of free Baxter algebras, Advances in Math., 9 (1972), 253-265.
  • A. Connes and D. Kreimer, Hopf algebras, renormalization and noncommuta- tive geometry, Comm. Math. Phys., 199(1) (1998), 203-242.
  • K. Ebrihimi-Fard, Loday-type algebras and the Rota-Baxter relation, Lett. Math. Phys., 61(2) (2002), 139-147.
  • K. Ebrahimi-Fard and L. Guo, Quasi-shues, mixable shues and Hopf alge- bras, J. Algebraic Combin., 24(1) (2006), 83-101.
  • K. Ebrahimi-Fard and L. Guo, Rota-Baxter algebras and dendriform algebras, J. Pure Appl. Algebra, 212(2) (2008), 320-339.
  • X. Gao, L. Guo and T. Zhang, Bialgebra and Hopf algebra structures on free Rota-Baxter algebra, arXiv:1604.03238.
  • L. Guo, An Introduction to Rota-Baxter Algebra, Surveys of Modern Mathematics, 4, International Press, Somerville, MA; Higher Education Press, Beijing, 2012.
  • L. Guo and W. Keigher, Baxter algebras and shue products, Adv. Math., 150(1) (2000), 117-149.
  • L. Guo and W. Y. Sit Enumeration and generating functions of Rota-Baxter words, Math. Comput. Sci., 4(2-3) (2010), 313-337.
  • R. Jian and J. Zhang, Rota-Baxter coalgebras, arXiv:1409.3052. [20] Y. Kosmann-Schwarzbach, Lie bialgebras, Poisson Lie groups and dressing transformations, in \Integrability of nonlinear systems", Lecture Notes in Phys., 495, Springer, Berlin, (1997), 104-170.
  • T. Ma and L. Liu, Rota-Baxter coalgebras and Rota-Baxter bialgebras, Linear Multilinear Algebra, 64(5) (2016), 968-979.
  • A. Makhlouf and D. Yau, Rota-Baxter Hom-Lie-admissible algebras, Comm. Algebra, 42(3) (2014), 1231-1257.
  • D. Manchon, Hoft algebras, from basics to applications to renormalization, Comptes-rendus des Rencontres mathematiques de Glanon, 2001.
  • M. Marcolli and X. Ni, Rota-Baxter algebras, singular hypersurfaces, and renormalization on Kausz compacti cations, J. Singul., 15 (2016), 80-117.
  • J. Pei, C. Bai and L. Guo, Splitting of operads and Rota-Baxter operators on operads, Appl. Categ. Structures, 25(4) (2017), 505-538.
  • G.-C. Rota, Baxter algebras and combinatorial identities I, II, Bull. Amer. Math. Soc., 75 (1969), 325-329, 330-334.
  • M. A. Semenov-Tian-Shansky, What is a classical R-matrix? Functional Anal. Appl. 17(4) (1983), 259-272.
  • T. Zhang, X. Gao and L. Guo, Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras, J. Math. Phys., 57(10) (2016), 101701 (16 pp).
  • X. Zhang, X. Gao and L. Guo, Commutative modi ed Rota-Baxter algebras, shuffe products and Hopf algebras, Bull. Malays. Math. Sci. Soc., (2018), https://doi.org/10.1007/s40840-018-0648-3.
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Xigou Zhang Bu kişi benim

Xing Gao Bu kişi benim

Li Guo Bu kişi benim

Yayımlanma Tarihi 8 Ocak 2019
Yayımlandığı Sayı Yıl 2019

Kaynak Göster

APA Zhang, X., Gao, X., & Guo, L. (2019). FREE MODIFIED ROTA-BAXTER ALGEBRAS AND HOPF ALGEBRAS. International Electronic Journal of Algebra, 25(25), 12-34. https://doi.org/10.24330/ieja.504101
AMA Zhang X, Gao X, Guo L. FREE MODIFIED ROTA-BAXTER ALGEBRAS AND HOPF ALGEBRAS. IEJA. Ocak 2019;25(25):12-34. doi:10.24330/ieja.504101
Chicago Zhang, Xigou, Xing Gao, ve Li Guo. “FREE MODIFIED ROTA-BAXTER ALGEBRAS AND HOPF ALGEBRAS”. International Electronic Journal of Algebra 25, sy. 25 (Ocak 2019): 12-34. https://doi.org/10.24330/ieja.504101.
EndNote Zhang X, Gao X, Guo L (01 Ocak 2019) FREE MODIFIED ROTA-BAXTER ALGEBRAS AND HOPF ALGEBRAS. International Electronic Journal of Algebra 25 25 12–34.
IEEE X. Zhang, X. Gao, ve L. Guo, “FREE MODIFIED ROTA-BAXTER ALGEBRAS AND HOPF ALGEBRAS”, IEJA, c. 25, sy. 25, ss. 12–34, 2019, doi: 10.24330/ieja.504101.
ISNAD Zhang, Xigou vd. “FREE MODIFIED ROTA-BAXTER ALGEBRAS AND HOPF ALGEBRAS”. International Electronic Journal of Algebra 25/25 (Ocak 2019), 12-34. https://doi.org/10.24330/ieja.504101.
JAMA Zhang X, Gao X, Guo L. FREE MODIFIED ROTA-BAXTER ALGEBRAS AND HOPF ALGEBRAS. IEJA. 2019;25:12–34.
MLA Zhang, Xigou vd. “FREE MODIFIED ROTA-BAXTER ALGEBRAS AND HOPF ALGEBRAS”. International Electronic Journal of Algebra, c. 25, sy. 25, 2019, ss. 12-34, doi:10.24330/ieja.504101.
Vancouver Zhang X, Gao X, Guo L. FREE MODIFIED ROTA-BAXTER ALGEBRAS AND HOPF ALGEBRAS. IEJA. 2019;25(25):12-34.