In this paper we show that for an n-Filippov algebra g, the tensor power g ^n-1 is endowed with a structure of anti-symmetric co-representation over the Leibniz algebra g ^n-1. This co-representation is used to define...In this paper we show that for an n-Filippov algebra g, the tensor power g ^n-1 is endowed with a structure of anti-symmetric co-representation over the Leibniz algebra g ^n-1. This co-representation is used to define some relative theories for Leibniz n-algebras with n 〉 2 and obtain exact sequences relating them. As a result, we construct a spectral sequence for the Leibniz homology of Filippov algebras.展开更多
Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure theory （such as （co）homology groups, universal central extensions） of Hom-Leibniz ...Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure theory （such as （co）homology groups, universal central extensions） of Hom-Leibniz algebras based on some works of Loday and Pirashvili.展开更多
文摘In this paper we show that for an n-Filippov algebra g, the tensor power g ^n-1 is endowed with a structure of anti-symmetric co-representation over the Leibniz algebra g ^n-1. This co-representation is used to define some relative theories for Leibniz n-algebras with n 〉 2 and obtain exact sequences relating them. As a result, we construct a spectral sequence for the Leibniz homology of Filippov algebras.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10825101, 11047030） and Natural Science Foundation of He＇nan Provincial Education Department （Grant No. 2010Bl10003）
文摘Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure theory （such as （co）homology groups, universal central extensions） of Hom-Leibniz algebras based on some works of Loday and Pirashvili.
