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(Co)Homology and Universal Central Extension of Hom-Leibniz Algebras 被引量:21
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作者 Yong Sheng CHENG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第5期813-830,共18页
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
关键词 Hom-Leibniz algebra (co)homology theory central extension
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Homological Perturbation Theory and Mirror Symmetry
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作者 JianZHOU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2003年第4期695-714,共20页
We explain how deformation theories of geometric objects such as complexstructures, Poisson structures and holomorphic bundle structures lead to differential Gerstenhaberor Poisson algebras. We use homological perturb... We explain how deformation theories of geometric objects such as complexstructures, Poisson structures and holomorphic bundle structures lead to differential Gerstenhaberor Poisson algebras. We use homological perturbation theory to construct A_∞ algebra structures onthe cohomology, and their canonically defined deformation. Such constructions are used to formulatea version of A_∞ algebraic mirror symmetry. 展开更多
关键词 homological perturbation theory mirror symmetry
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