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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. https://resolver.caltech.edu/CaltechAUTHORS:20140219-083726921

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.jalgebra.2013.12.003 DOIArticle
http://www.sciencedirect.com/science/article/pii/S0021869313006546PublisherArticle
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).
Funders:
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
SRFDP200800550015
SRFDP20120031110022
Subject Keywords:Lie algebra; Pre-Lie algebra; L-dendriform algebra; Hessian structure
Classification Code:MSC: 17A30; 17B05; 17B60
Record Number:CaltechAUTHORS:20140219-083726921
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140219-083726921
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, http://dx.doi.org/10.1016/j.jalgebra.2013.12.003. (http://www.sciencedirect.com/science/article/pii/S0021869313006546)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:43865
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 Feb 2014 22:33
Last Modified:03 Oct 2019 06:12

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