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| 1 | Note on Co-split Lie Algebras显示文摘It is proved that,any finite dimensional complex Lie algebra L = [L,L],hence,over a field of characteristic zero,any finite dimensional Lie algebra L = [L,L] possessing a basis with complex structure constants,should be a weak co-split Lie algebra.A class of non-semi-simple co-split Lie algebras is given. | Limeng XIA | 2012 | Chinese Annals of Mathematics,Series B2012，33，5： | 4 |
| 2 | On the centers of quantum groups of A_n-type显示文摘Let g be the finite dimensional simple Lie algebra of type A_n, and let U = U_q(g,Λ)and U= U_q(g,Q)be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find two algebraically independent central elements in U for all n ≥ 2 and give an explicit formula of the Casimir elements for the quantum group U = U_q(g,Λ), which corresponds to the Casimir element of the enveloping algebra U(g). Moreover, for n = 2 we give explicitly generators of the center subalgebras of the quantum groups U = U_q(g,Λ) and U = U_q(g,Q). | Libin Li Limeng Xia Yinhuo Zhang | 2018 | Science China Mathematics2018，61，2： | 2 |
| 3 | The importance of coil conductivity and eddy current effects in the analysis of electromagnetic forming process显示文摘Coil design and performance analysis are critical for the electromagnetic forming(EMF)process.However,previous studies have paid little attention to the coil con-ductivity,and the influence of eddy current effects in coil conductors on the forming process has not been well understood.This work aims to address these problems through numerical and experimental investigations.It is found that,due to the eddy current effects,the uneven current distribution appears in the coil conductors that should be considered when analysing the forming process,especially for the cases with large heights of coil conductors.Meanwhile,an important and interesting discovery is that the eddy current effects can greatly reduce the sensitivity of the coil conductivity with respect to the workpiece deformation,the Joule heating and the temperature rise in the coil.For instance,compared to a forming system with a copper coil,the forming height of the workpiece in the forming system with an AA5083‐O coil is reduced by less than 5%under the same discharge energy,while the copper conductivity is 3.3 times that of the latter.These results are helpful to understand the EMF process and achieve the optimal design of coils. | Quanliang Cao Liangyu Xia Xian Li Limeng Du Zhipeng Lai Xiaotao Han Liang Li | 2022 | High Voltage2022，7，2： | 1 |
| 4 | Global existence for the higher-order Camassa-Holm shallow water equation显示文摘 | Tian Lixin Zhang Ping Xia Limeng | 2011 | Nonlinear Analysis2011，74，： | 1 |
| 5 | Majid conjecture: quantum Kac-Moody algebras version显示文摘Based on the n-fold tensor product version of the generalized double-bosonization construction,we prove the Majid conjecture of the quantum Kac-Moody algebras version.Particularly,we give explicitly the double-bosonization type-crossing constructions of quantum Kac-Moody algebras for affine types G(1)2,E(1)6,and Tp,q,r,and in this way,we can recover generators of quantum Kac-Moody algebras with braided groups defined by R-matrices in the related braided tensor category.This gives us a better understanding for the algebra structures themselves of the quantum Kac-Moody algebras as a certain extension of module-algebras/module-coalgebras with respect to the related quantum subalgebras of finite types inside. | Hongmei HU Naihong HU Limeng XIA | 2021 | Frontiers of Mathematics in China2021，16，3： | 1 |
| 6 | Classification on irreducible Whittaker modules over quantum group Uq(sl3,∧)显示文摘We define the Whittaker modules over the simply-connected quantum group U_(q)(sl3,∧),where A is the weight lattice of Lie algebra sl3.Then we completely classify all those simple ones.Explicitly,a simple Whittaker module over U_(q)(sl3,∧)is either a highest weight module,or determined by two parameters z∈C andγ∈C^(*)(up to a Hopf automorphism). | Limeng XIA Xiangqian GUO Jiao ZHANG | 2021 | Frontiers of Mathematics in China2021，16，4： | 0 |
| 7 | Twisted Whittaker modules over U_(q)(gl_(n+1))显示文摘As is well known,the classical nonsingular Whittaker modules over quantum groups cannot be defined for the non-A1 type.In this paper,by choosing different generators for the quantum group U_(q)(gl_(n+1)),we introduce and study the twisted Whittaker modules over U_(q)(gl_(n+1)).We classify all the simple twisted Whittaker modules with nonsingular Whittaker functions.This agrees with Kostant’s results on Whittaker modules for the simple complex Lie algebras sln+1 as q approaches 1. | Limeng Xia Kaiming Zhao | 2023 | Science China Mathematics2023，66，10： | 0 |
| 8 | Finite dimensional modules over quantum toroidal algebras显示文摘For all generic q∈C^∗,when g is not of type A1;we prove that the quantum toroidal algebra Uq(gtor)has no nontrivial finite dimensional simple module. | Limeng XIA | 2020 | Frontiers of Mathematics in China2020，15，3： | 0 |
| 9 | The Polynomial Modules over Quantum Group U_(q)(sl3)显示文摘Let g be a finite dimensional complex simple Lie algebra with Cartan subalgebraη.Then C[η]has a g-module structure if and only if g is of type A or of type C;this is called the polynomial module of rank one,In the quantum version,the rank one polynomial modules over U_(q)(sl_(2))have been classified.In this paper,we prove that the quantum group U_(q)(sl_(3))has no rank one polynomial module. | Limeng Xia Qianqian Cai Jiao Zhang | 2022 | Algebra Colloquium2022，29，4： | 0 |
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