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

The roles of radiative, structural and physiological information of sun-induced chlorophyll fluorescence in predicting gross primary production of a corn crop at various temporal scales

Extensive research suggests that sun-induced chlorophyll fluorescence (SIF) and gross primary productivity (GPP) have a near-linear relationship, providing a promising avenue for estimating the carbon uptake of ecosystems. However, the factors influencing the relationship are not yet clear. This study examines the roles of SIF's radiative, structural, and physiological information in predicting GPP, based on four years of field observations of a corn canopy at various temporal scales. We quantified SIF's radiative component by measuring the intensity of incident photosynthetically active radiation (iPAR), and separated the structural and physiological components from SIF observations using the fluorescence correction vegetation index (FCVI). Our results show that the R2 values between SIF and GPP, as estimated by linear models, increased from 0.66 at a half-hour resolution to 0.86 at a one-month resolution. In comparison, the product of FCVI and iPAR, representing the non-physiological information of SIF, performed consistently well in predicting GPP with R2&gt;0.84 at various temporal scales, suggesting a limited contribution of the physiological information of SIF for GPP estimation. The results further reveal that SIF's radiative and structural components positively impacted the SIF-GPP linearity, while the physiological component had a negative impact on the linearity for most cases, changing from 0.6 % to -27.5 %. As for the temporal dependency, the controls of the SIF-GPP relationship moved from radiation at diurnal scales to structure at the seasonal scales. The structural contribution changed from 14.8 % at a half-hour resolution to 92.4 % at a one-month resolution, while the radiative contribution decreased from 118.0 % at a half-hour resolution to 11.7 % at a one-month resolution. This study contributes to enhancing our understanding of the physiological information conveyed by SIF and the factors influencing the temporal dependency of the SIF-GPP relationship.</p

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