On the Toroidal Leibniz Algebras
Acta Mathematica Sinica, English Series
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Acta Mathematica Sinica, English Series  2008, Vol. 24 Issue (2): 227-240    DOI: 10.1007/s10114-007-1003-z
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On the Toroidal Leibniz Algebras
Dong LIU1, Lei LIN2
1. Department of Mathematics, Huzhou Teachers College, Huzhou, 313000, P. R. China;
2. Department of Mathematics, East China Normal University, Shanghai, 200062, P. R. China
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Abstract Toroidal Leibniz algebras are the universal central extensions of the iterated loop algebras ġ⊕C[t1±1 ,...,tv±1 ] in the category of Leibniz algebras. In this paper, some properties and representations of toroidal Leibniz algebras are studied. Some general theories of central extensions of Leibniz algebras are also obtained.
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Dong LIU
Key wordsToroidal Leibniz algebra   derivation and automorphism   universal central extension     
Received: 2005-07-15;
Fund: D. Liu is supported by the NNSF (Grants 10671027, 10271076, 10701019), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 06KJB110003). L. Lin is supported in part by Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT), and the Shanghai Priority Academic Discipline from the SMEC
Cite this article:   
Dong LIU,Lei LIN. On the Toroidal Leibniz Algebras[J]. Acta Mathematica Sinica, English Series, 2008, 24(2): 227-240.
http://www.actamath.com/Jwk_sxxb_en//EN/10.1007/s10114-007-1003-z      or     http://www.actamath.com/Jwk_sxxb_en//EN/Y2008/V24/I2/227
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