JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (10): 38-44.doi: 10.6040/j.issn.1671-9352.0.2014.265

Previous Articles     Next Articles

Kegel theorem for generalized Lie algebras

CHEN Hua-xi1, ZHANG Cui-bin1, DONG Li-hong2   

  1. 1. Department of Mathematics and Physics, Bengbu College, Bengbu 233000, Anhui, China;
    2. College of Mathematics and Science, Henan Normal University, Xinxiang, 453007, Henan, China
  • Received:2014-06-12 Online:2014-10-20 Published:2014-11-10

PDF (PC)

436

Abstract: Let π be a group and H,σa cotriangular Hopf πcoalgebra. The difinitions of a class of generalized Lie algebras in the category of right π-comodules over H are introduced, and an analogue of the classical Kegel's theorem is obtained.

Key words: Kegel theorem, π-H-comudule algebras, Hopf π-coalgebras

CLC Number: 

  • O153
[1] KEGEL O H. Zur Nilpotenz gewisser assoziative ringe[J]. Mathematische Annalen, 1963, 149:258-260.
[2] BAHTURIN Y, GIAMBRUNO A. Identities of sum of commutative subalgebras, rendiconti[J]. Circolo del Mathematico di Palermo Ser, 1994, 243:250-258.
[3] BAHTURIN Y, KEGEL O H. Universal sums of abelian subalgebras[J]. Comm Algebra, 1995, 23:2975-2990.
[4] BAHTURIN Y, FISCHMAN D, MONTGOMERY S. On the generalized Lie structure of associative algebras[J]. Israel J of Math, 1996, 96:27-48.
[5] FISHMAN D, MONTGOMERY S. A Schur's double centealizer theorem for cotriangular Hopf algebras and generalized Lie algerbas[J]. J Algebra, 1994,168(2):594-614.
[6] SWEEDLER M E. Hopf algebras[M]. New York: Benjamin, 1969: 3-90.
[7] TURAEV V G. Homotopy field theory in dimension 3 and crossed group-categories[EB/OL]. http://arxiv.org/abs/math/0005291:1-76.
[8] VIRELIZIER A. Hopf group-coalgebras[J]. J Pure and Applied Algebra, 2002, 171:75-122.
[9] WANG Shuanhong. Group twisted smash products and Doi-Hopf modules for T-coalgebras[J]. Comm Algebra, 2004, 32(9):3417-3436.
[10] WANG Shuanhong. Group entwining structures and group coalgebra Galois extensions[J]. Comm Algebra, 2004, 32(9):3437-3458.
[11] ZHU Meiling, CHEN Huixiang, LI Libin. Coquasitriangular Hopf group coalgebras and braided monoidal categories[J]. Front Math China, 2011, 6(5):1009-1020.
[12] ZUNINO M. Double construction for crossed Hopf coalgebra[J]. J Algebra, 2004, 278:43-75.
[13] ZUNINO M. Yetter-Drinfeld modules for crossed structures[J]. J Pure and Applied Algebra, 2004,193(1-3):313-343.
[1] WU Xiao-ying, WANG Fang-gui. Graded version of Enochs theorem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 22-26.
[2] . Representative forms of commutative BR0-algebras on a set by implication operator [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 86-94.
[3] CHENG Cheng, ZOU Shi-jia. Irreducible splitting trace module of a class of Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 11-15.
[4] LIU Chun-hui. On(∈,∈∨q(λ, μ))-fuzzy LI-ideals in lattice implication algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 65-72.
[5] WANG Hai-wei, ZHAO Bin. The projective objects in the category of Q-sup-algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 73-82.
[6] ZHU Lin. Separated monic representations of quivers of type A4and RSS equivalences [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 1-8.
[7] PENG Jia-yin. Falling fuzzy filters on residuated lattices [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 52-64.
[8] GUO Shuang-jian, LI Yi-zheng. When is BHQ a pre-braided category over quasi-Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 10-15.
[9] LU Dao-wei, WANG Zhen. L-R smash product for bialgebroids [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 32-35.
[10] LI Jin-lan, LIANG Chun-li. Strongly Gorenstein C-flat modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 25-31.
[11] WANG Hui-xing, CUI Jian, CHEN Yi-ning. Nil *-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 16-24.
[12] SUN Yan-zhong, YANG Xiao-yan. Gorenstein AC-projective modules with respect to a semidualizing module [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 31-35.
[13] MA Xin, ZHAO You-yi, NIU Xue-na. Homology resolutions and homological dimensions of complexes [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 18-23.
[14] LIU Chun-hui. Lattice of(,∨(-overq))-fuzzy filters in a BL-algebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 104-110.
[15] . Gelfand-Krillov dimension of quantized enveloping algebra Uq(An) [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 12-17.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd