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COASSOCIATIVE LIE ALGEBRAS

Published online by Cambridge University Press:  01 October 2013

D.-G. WANG ,
J. J. ZHANG  and
G. ZHUANG
D.-G. WANG
Affiliation:
School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, P. R. China e-mail: dgwang@mail.qfnu.edu.cn
J. J. ZHANG
Affiliation:
Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195, USA e-mail: zhang@math.washington.edu
G. ZHUANG
Affiliation:
e-mail: gzhuang@math.washington.edu
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Abstract

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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).

Keywords

Primary 16A2416W3057T05

References

REFERENCES

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.CrossRefGoogle Scholar
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.Koszul, J.-J., Homologie et cohomologie des algébres de Lie, Bull. Soc. Math. France 78 (1950), 65–127.Google Scholar
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.Lu, D.-M., Wu, Q.-S. and Zhang, J. J., Homological integral of Hopf algebras, Trans. Amer. Math. Soc. 359 (10) (2007), 4945–4975.CrossRefGoogle Scholar
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.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.Yekutieli, A., The rigid dualizing complex of a universal enveloping algebra, J. Pure Appl. Algebra 150 (2000), 85–93.Google Scholar
9.Zhuang, G., Existence of Hopf subalgebras of GK-dimension two, J. Pure Appl. Algebra 215 (2011), 2912–2922.Google Scholar
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