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Pseudo-Hessian Lie algebras and L-dendriform bialgebras

Ni, Xiang and Bai, Chengming (2014) Pseudo-Hessian Lie algebras and L-dendriform bialgebras. Journal of Algebra, 400 . pp. 273-289. ISSN 0021-8693.

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In this paper, we study a special class of pseudo-Hessian Lie algebras satisfying an additional condition that they are decomposed into a direct sum of underlying vector spaces of two Lagrangian subalgebras in terms of L-dendriform algebras which are the underlying algebraic structures. Such structures are equivalent to certain bialgebra structures, namely, L-dendriform bialgebras. Furthermore, we introduce and study the so-called triangular pseudo-Hessian Lie algebras and relate them to some semidirect product constructions from the “Lie-type” operations of L-dendriform algebras.

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Additional Information:© 2013 Elsevier Inc. Received 15 August 2010; Available online 24 December 2013. Communicated by Efim Zelmanov. This work is supported in part by NSFC (10921061, 11271202, 11221091), NKBRPC (2006CB 805905) and SRFDP (200800550015, 20120031110022).
Funding AgencyGrant Number
National Natural Science Foundation of China (NSFC)10921061
National Natural Science Foundation of China (NSFC)11271202
National Natural Science Foundation of China (NSFC)11221091
NKBRPC2006CB 805905
Subject Keywords:Lie algebra; Pre-Lie algebra; L-dendriform algebra; Hessian structure
Classification Code:MSC: 17A30; 17B05; 17B60
Record Number:CaltechAUTHORS:20140219-083726921
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Official Citation:Xiang Ni, Chengming Bai, Pseudo-Hessian Lie algebras and L-dendriform bialgebras, Journal of Algebra, Volume 400, 15 February 2014, Pages 273-289, ISSN 0021-8693, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:43865
Deposited By: Tony Diaz
Deposited On:20 Feb 2014 22:33
Last Modified:03 Oct 2019 06:12

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