In this paper,all symmetric super-biderivations of some Lie superalgebras are determined.As an application,commutative post-Lie super algebra structures on these Lie super algebras are also obtained.
Lithium ion batteries(LIBs)have dominated the portable electric market over decades;however,the limited and unevenly distributed lithium resources induce concerns on their future large-scale applications.Increasing ef...Lithium ion batteries(LIBs)have dominated the portable electric market over decades;however,the limited and unevenly distributed lithium resources induce concerns on their future large-scale applications.Increasing efforts have been endeavored on exploring post-Li ion batteries,such as Na-ion,K-ion,Al-ion and Mg-ion batteries,due to the high abundance of the corresponding elements in Earth crust.Manufacturing reliable electrode materials is the key to develop these new battery systems.Facile and scalable electrospinning has been widely utilized in preparing mechanically stable,flexible and conductive nanofiber electrodes as successfully proven in LIBs.In recent years,tremendous efforts have been devoted to electrospinning nanofiber electrodes for post-Li ion batteries and discernible progress in the electrochemical performance has been witnessed.Herein,we aim to review the-state-of-the-art advances made in electrospun nanofiber materials in optimizing post-Li ion battery technology by surveying the correlations among the morphology,the surface chemistry,the structure of electrospun nanofibers,and the post-Li ion batteries performance.Based on intensive investigations and insightful understandings,perspectives to the future design of electrospun nanofiber electrodes are also presented.展开更多
Let sv be the extended Schrödinger–Virasoro Lie algebra and n≥1 an integer.A map f:svn=sv×sv×⋯×sv→sv is called an n-derivation if it is a derivation in one variable while other variables fixed.W...Let sv be the extended Schrödinger–Virasoro Lie algebra and n≥1 an integer.A map f:svn=sv×sv×⋯×sv→sv is called an n-derivation if it is a derivation in one variable while other variables fixed.We investigate n-derivations of the extended Schrödinger–Virasoro Lie algebra sv.The main result when n=2 is then applied to characterize the linear commuting maps and the commutative post-Lie algebra structures on sv.展开更多
Let L be a simple modular Lie superealgebra of Witt type or special type over an algebraically closed field of characteristic p>2.In this paper,all the super-biderivations of L are studied.By means of weight space ...Let L be a simple modular Lie superealgebra of Witt type or special type over an algebraically closed field of characteristic p>2.In this paper,all the super-biderivations of L are studied.By means of weight space decompositions with respect to a suitable torus and the standard Z-grading structures of L,we show that the super-symmetric superbiderivations of L are zero.Generalizing a result on the skewsymmetric biderivation of Lie algebras to the super case,we find that all the superbiderivations of L are inner.As applications,the linear supercommuting maps and the supercommutative post-Lie superalgebra structures on L are described.展开更多
This paper studies the concepts of a totally compatible dialgebra and a totally compatible Lie dialgebra,defined to be a vector space with two binary operations that satisfy individual and mixed associativity conditio...This paper studies the concepts of a totally compatible dialgebra and a totally compatible Lie dialgebra,defined to be a vector space with two binary operations that satisfy individual and mixed associativity conditions and Lie algebra conditions respectively.We show that totally compatible dialgebras are closely related to bimodule algebras and semi-homomorphisms.More significantly,Rota-Baxter operators on totally compatible dialgebras provide a uniform framework to generalize known results that Rota-Baxter related operators give tridendriform algebras.Free totally compatible dialgebras are constructed.We also show that a Rota-Baxter operator on a totally compatible Lie dialgebra gives rise to a PostLie algebra,generalizing the fact that a Rota-Baxter operator on a Lie algebra gives rise to a PostLie algebra.展开更多
基金Supported by NNSF(Grant Nos.12071405,11971315)Xinjiang Uygur Autonomous Region graduate scientific research innovation project(Grant No.XJ2021G021)。
文摘In this paper,all symmetric super-biderivations of some Lie superalgebras are determined.As an application,commutative post-Lie super algebra structures on these Lie super algebras are also obtained.
基金supported by a grant from the Research Committee of The Hong Kong Polytechnic University under project code 1-BE3M.
文摘Lithium ion batteries(LIBs)have dominated the portable electric market over decades;however,the limited and unevenly distributed lithium resources induce concerns on their future large-scale applications.Increasing efforts have been endeavored on exploring post-Li ion batteries,such as Na-ion,K-ion,Al-ion and Mg-ion batteries,due to the high abundance of the corresponding elements in Earth crust.Manufacturing reliable electrode materials is the key to develop these new battery systems.Facile and scalable electrospinning has been widely utilized in preparing mechanically stable,flexible and conductive nanofiber electrodes as successfully proven in LIBs.In recent years,tremendous efforts have been devoted to electrospinning nanofiber electrodes for post-Li ion batteries and discernible progress in the electrochemical performance has been witnessed.Herein,we aim to review the-state-of-the-art advances made in electrospun nanofiber materials in optimizing post-Li ion battery technology by surveying the correlations among the morphology,the surface chemistry,the structure of electrospun nanofibers,and the post-Li ion batteries performance.Based on intensive investigations and insightful understandings,perspectives to the future design of electrospun nanofiber electrodes are also presented.
基金This work was supported in part by the NSFC(No.11771069)the NSF of Heilongjiang Province(No.LH2020A020)the Fund of Heilongjiang Provincial Laboratory of the Theory and Computation of Complex Systems。
文摘Let sv be the extended Schrödinger–Virasoro Lie algebra and n≥1 an integer.A map f:svn=sv×sv×⋯×sv→sv is called an n-derivation if it is a derivation in one variable while other variables fixed.We investigate n-derivations of the extended Schrödinger–Virasoro Lie algebra sv.The main result when n=2 is then applied to characterize the linear commuting maps and the commutative post-Lie algebra structures on sv.
基金supported by NSF of China(12061029)and NSF of Heilongjiang Province(LH2022A019)supported by NSF of China(12061029)NSF of Hainan Province(120RC587).
文摘Let L be a simple modular Lie superealgebra of Witt type or special type over an algebraically closed field of characteristic p>2.In this paper,all the super-biderivations of L are studied.By means of weight space decompositions with respect to a suitable torus and the standard Z-grading structures of L,we show that the super-symmetric superbiderivations of L are zero.Generalizing a result on the skewsymmetric biderivation of Lie algebras to the super case,we find that all the superbiderivations of L are inner.As applications,the linear supercommuting maps and the supercommutative post-Lie superalgebra structures on L are described.
基金supported by National Natural Science Foundation of China(Grant Nos.10920161,11271202,11221091 and 11371178)Specialized Research Fund for the Doctoral Program of Higher Education(Grant Nos.200800550015 and 20120031110022)National Science Foundation of USA(Grant No.DMS-1001855)
文摘This paper studies the concepts of a totally compatible dialgebra and a totally compatible Lie dialgebra,defined to be a vector space with two binary operations that satisfy individual and mixed associativity conditions and Lie algebra conditions respectively.We show that totally compatible dialgebras are closely related to bimodule algebras and semi-homomorphisms.More significantly,Rota-Baxter operators on totally compatible dialgebras provide a uniform framework to generalize known results that Rota-Baxter related operators give tridendriform algebras.Free totally compatible dialgebras are constructed.We also show that a Rota-Baxter operator on a totally compatible Lie dialgebra gives rise to a PostLie algebra,generalizing the fact that a Rota-Baxter operator on a Lie algebra gives rise to a PostLie algebra.
