[1] Chen Xiuli, Li Fang, Chen Jianlong,. Hom-dimodules and FRT theorem of Hom type [J]. Journal of Southeast University (English Edition), 2014, 30 (3): 391-395. [doi:10.3969/j.issn.1003-7985.2014.03.025]

Copy

Hom-dimodules and FRT theorem of Hom type()

Share：

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

30

Issue:

2014 3

Page:

391-395

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2014-09-30

Info

Title:

Hom-dimodules and FRT theorem of Hom type

Author(s):

Chen Xiuli¹;  Li Fang²;  Chen Jianlong¹

¹Department of Mathematics, Southeast University, Nanjing 211189, China
²Department of Mathematics, Zhejiang University, Hangzhou 310028, China

Keywords:

Hom-bialgebra;  Hom-dimodule;  Hom D-equation

PACS:

O153

DOI:

10.3969/j.issn.1003-7985.2014.03.025

Abstract:

In order to study the deformation of algebras, the notions of Hom-algebras are introduced. The Hom-algebra is a generalization of the classical associative algebra. First, the Hom-type generalization of dimodules, which is called the Hom-dimodule, is introduced, and its properties are discussed Moreover, the category of Hom-dimodules in connection with the Hom D-equation R¹²R²³=R²³R¹²for R∈End_kk(M⊗M)and a Hom-module M is investigated. Some solutions of the Hom D-equation from Hom-dimodules over Hom-bialgebras are given, and the FRT-type theorem is constructed in the category of Hom-dimodules. The results generalize and improve the FRT-type theorem in the category of dimodules.

References:

[1] Long F W. The Brauer group of dimodule algebras [J]. Journal of Algebra, 1974, 31(1/2/3): 559-601.
[2] Caenepeel C, Militaru G, Zhu S L. Crossed modules and Doi-Hopf modules [J]. Israel Journal of Mathematics, 1997, 100(4): 221-247.
[3] Militaru G. The long dimodules category and nonlinear equations [J]. Algebras and Representation Theory, 1999, 2(2): 177-200.
[4] Larsson D, Silvestrov S D. Quasi-Hom-Lie algebras, central extensions and 2-cocycle-like identities [J]. Journal of Algebra, 2005, 288(2): 321-344.
[5] Makhlouf A, Silvestrov S. Hom-algebra structures [J]. Journal of Generalized Lie Theory and Applications, 2008, 2(2): 51-64.
[6] Makhlouf A, Silvestrov S. Hom-Lie admissible Hom-coalgebras and Hom-Hopf algebras [M]//Generalized Lie theory in mathematics, physics and beyond. Berlin: Springer, 2009:189-206.
[7] Makhlouf A, Silvestrov S. Hom-algebras and Hom-coalgebras [J]. Journal of Algebra and Its Applications, 2010, 9(4): 1-37.
[8] Yau D. Hom-bialgebras and comodule Hom-algebras [J]. International Electronic Journal of Algebra, 2010, 8: 45-64.
[9] Yau D. The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras [EB/OL].(2009-05-12)[2013-02-27]. http://arxiv.org/abs/0905.1890.
[10] Yau D. The Hom-Yang-Baxter equation, Hom-Lie algebras, and quasi-triangular bialgebras [J]. Journal of Physics A, 2009, 42(16):165202-1-165202-12.
[11] Yau D. The Hom-Yang-Baxter equation and Hom-Lie algebras [J]. Journal of Mathematical Physics, 2011, 52(5): 053502-1-053502-19.
[12] Yau D. Hom-quantum groups Ⅰ: quasi-triangular Hom-bialgebras [J]. Journal of Physics A, 2012, 45(6): 065203-1-065203-23.
[13] Yau D. Hom-quantum groups Ⅱ: cobraided Hom-bialgebras and Hom-quantum geometry [EB/OL].(2009-07-10)[2013-02-27]. http://arxiv.org/abs/0907.1880.
[14] Yau D. Enveloping algebras of Hom-Lie algebras [J]. Journal of Generalized Lie Theory and Applications, 2008, 2(2): 95-108.

Memo

Memo:

Biographies: Chen Xiuli(1980—), female, doctor; Chen Jianlong(corresponding author), male, doctor, professor, jlchen@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.11371089), the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020), the Postdoctoral Innovation Funds of Southeast University(No.3207013601).
Citation: Chen Xiuli, Li Fang, Chen Jianlong.Hom-dimodules and FRT theorem of Hom type[J].Journal of Southeast University(English Edition), 2014, 30(3):391-395.[doi:10.3969/j.issn.1003-7985.2014.03.025]

Common functions