Cohomologies of pre-LieDer pairs and applications

In this paper, we use the higher derived bracket to give the controlling algebra of pre-LieDer pairs. We give the cohomology of pre-LieDer pairs by using the twist $L_\infty$-algebra of this controlling algebra. In particular, we define the cohomology of regular pre-LieDer pairs. We study infinitesimal deformations of pre-LieDer pairs, which are characterized by the second cohomology group of pre-LieDer pairs. We also define the cohomology of regular pre-LieDer pairs with coefficients in arbitrary representation and using the second cohomology group to classify abelian extensions of regular pre-LieDer pairs

Deformations and abelian extensions of compatible pre-Lie algebras

In this paper, we first give the notation of a compatible pre-Lie algebra and its representation. We study the relation between compatible Lie algebras and compatible pre-Lie algebras. We also construct a new bidifferential graded Lie algebra whose Maurer-Cartan elements are compatible pre-Lie structures. We give the bidifferential graded Lie algebra which controls deformations of a compatible pre-Lie algebra. Then, we introduce a cohomology of a compatible pre-Lie algebra with coefficients in itself. We study infinitesimal deformations of compatible pre-Lie algebras and show that equivalent infinitesimal deformations are in the same second cohomology group. We further give the notion of a Nijenhuis operator on a compatible pre-Lie algebra. We study formal deformations of compatible pre-Lie algebras. If the second cohomology group \huaH^2(\g;\g) is trivial, then the compatible pre-Lie algebra is rigid. Finally, we give a cohomology of a compatible pre-Lie algebra with coefficients in arbitrary representation and study abelian extensions of compatible pre-Lie algebras using this cohomology. We show that abelian extensions are classified by the second cohomology group.Comment: arXiv admin note: text overlap with arXiv:2301.06917; text overlap with arXiv:2208.12647, arXiv:2004.02098 by other author

The Centroid of a Lie Triple Algebra

General results on the centroids of Lie triple algebras are developed. Centroids of the tensor product of a Lie triple algebra and a unitary commutative associative algebra are studied. Furthermore, the centroid of the tensor product of a simple Lie triple algebra and a polynomial ring is completely determined

Does metal pollution matter with C retention by rice soil?

Date of Acceptance: 17/07/2015 The research work was supported by the China Natural Science Foundation under a grant number of 40830528 and of 40671180. P.S. is a Royal Scoiety-Wolfson Research Merit Award holder and was supported by additional travel funds from a UK BBSRC China Partnership Award. P.S.’s contribution was supported by the UK-China Sustainable Agriculture Innovation Network (SAIN). D.C. was supported by an additional travel and collaboration funding from the China Ministry of Education under a “111” project.Peer reviewedPublisher PD

The Influences of Drought and Land-Cover Conversion on Inter-Annual Variation of NPP in the Three-North Shelterbelt Program Zone of China Based on MODIS Data

Terrestrial ecosystems greatly contribute to carbon (C) emission reduction targets through photosynthetic C uptake.Net primary production (NPP) represents the amount of atmospheric C fixed by plants and accumulated as biomass. The Three-North Shelterbelt Program (TNSP) zone accounts for more than 40% of China’s landmass. This zone has been the scene of several large-scale ecological restoration efforts since the late 1990s, and has witnessed significant changes in climate and human activities.Assessing the relative roles of different causal factors on NPP variability in TNSP zone is very important for establishing reasonable local policies to realize the emission reduction targets for central government. In this study, we examined the relative roles of drought and land cover conversion(LCC) on inter-annual changes of TNSP zone for 2001–2010. We applied integrated correlation and decomposition analyses to a Standardized Evapotranspiration Index (SPEI) and MODIS land cover dataset. Our results show that the 10-year average NPP within this region was about 420 Tg C. We found that about 60% of total annual NPP over the study area was significantly correlated with SPEI (p<0.05). The LCC-NPP relationship, which is especially evident for forests in the south-central area, indicates that ecological programs have a positive impact on C sequestration in the TNSP zone. Decomposition analysis generally indicated that the contributions of LCC, drought, and other Natural or Anthropogenic activities (ONA) to changes in NPP generally had a consistent distribution pattern for consecutive years. Drought and ONA contributed about 74% and 23% to the total changes in NPP, respectively, and the remaining 3% was attributed to LCC. Our results highlight the importance of rainfall supply on NPP variability in the TNSP zone