Geodesic
COASSOCIATIVE LIE ALGEBRAS
Glasgow mathematical journal, Tome 55 (2013) no. A, pp. 195-215

Voir la notice de l'article provenant de la source Cambridge University Press

A coassociative Lie algebra is a Lie algebra equipped with a coassociative coalgebra structure satisfying a compatibility condition. The enveloping algebra of a coassociative Lie algebra can be viewed as a coalgebraic deformation of the usual universal enveloping algebra of a Lie algebra. This new enveloping algebra provides interesting examples of non-commutative and non-cocommutative Hopf algebras and leads to the classification of connected Hopf algebras of Gelfand–Kirillov dimension four in Wang et al. (Trans. Amer. Math. Soc., to appear).
DOI : 10.1017/S001708951300058X
Mots-clés : Primary 16A24, 16W30, 57T05 
WANG, D.-G.; ZHANG, J. J.; ZHUANG, G. COASSOCIATIVE LIE ALGEBRAS. Glasgow mathematical journal, Tome 55 (2013) no. A, pp. 195-215. doi: 10.1017/S001708951300058X
@article{10_1017_S001708951300058X,
     author = {WANG, D.-G. and ZHANG, J. J. and ZHUANG, G.},
     title = {COASSOCIATIVE {LIE} {ALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {195--215},
     year = {2013},
     volume = {55},
     number = {A},
     doi = {10.1017/S001708951300058X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951300058X/}
}
TY  - JOUR
AU  - WANG, D.-G.
AU  - ZHANG, J. J.
AU  - ZHUANG, G.
TI  - COASSOCIATIVE LIE ALGEBRAS
JO  - Glasgow mathematical journal
PY  - 2013
SP  - 195
EP  - 215
VL  - 55
IS  - A
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708951300058X/
DO  - 10.1017/S001708951300058X
ID  - 10_1017_S001708951300058X
ER  - 
%0 Journal Article
%A WANG, D.-G.
%A ZHANG, J. J.
%A ZHUANG, G.
%T COASSOCIATIVE LIE ALGEBRAS
%J Glasgow mathematical journal
%D 2013
%P 195-215
%V 55
%N A
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708951300058X/
%R 10.1017/S001708951300058X
%F 10_1017_S001708951300058X

[1] 1.Brown, K. A. and Zhang, J. J., Prime regular Hopf algebras of GK-dimension one, Proc. London Math. Soc. 101 (3) (2010), 260–302. Google Scholar | DOI

[2] 2.He, J.-W., Van Oystaeyen, F. and Zhang, Y., Co-commutative Calabi–Yau Hopf algebras and deformations, J. Algebra 324 (2010), 1921–1939. Google Scholar

[3] 3.Koszul, J.-J., Homologie et cohomologie des algébres de Lie, Bull. Soc. Math. France 78 (1950), 65–127. Google Scholar

[4] 4.Krause, G. R. and Lenagan, T. H., Growth of algebras and Gelfand–Kirillov dimension, Revised ed, Graduate Studies in Mathematics, 22 (American Mathematical Society, Providence, RI, 2000). Google Scholar

[5] 5.Lu, D.-M., Wu, Q.-S. and Zhang, J. J., Homological integral of Hopf algebras, Trans. Amer. Math. Soc. 359 (10) (2007), 4945–4975. Google Scholar | DOI

[6] 6.Montgomery, S., Hopf Algebras and their actions on rings, CBMS Regional Conference Series in Mathematics, 82 (American Mathematical Society, Providence, RI, 1993). Google Scholar

[7] 7.Wang, D.-G., Zhang, J. J. and Zhuang, G.-B., Classification of connected Hopf algebras of GK dimension four, Trans. Amer. Math. Soc. (to appear). Google Scholar

[8] 8.Yekutieli, A., The rigid dualizing complex of a universal enveloping algebra, J. Pure Appl. Algebra 150 (2000), 85–93. Google Scholar

[9] 9.Zhuang, G., Existence of Hopf subalgebras of GK-dimension two, J. Pure Appl. Algebra 215 (2011), 2912–2922. Google Scholar

[10] 10.Zhuang, G., Properties of pointed and connected Hopf algebras of finite Gelfand–Kirillov dimension, J. London Math. Soc. 87 (2) (2013), 877–898. Google Scholar

Cité par Sources :