白承铭
主要从事李理论和数学物理方面的研究,特别是侧重研究与李理论和数学物理相关的一些代数体系的结构及其应用。
个性化签名
- 姓名:白承铭
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学术头衔:
博士生导师
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学科领域:
数理逻辑与数学基础
- 研究兴趣:主要从事李理论和数学物理方面的研究,特别是侧重研究与李理论和数学物理相关的一些代数体系的结构及其应用。
白承铭,1971年6月生于黑龙江省双城,1992年本科毕业于南开大学数学专业,1997年毕业于南开大学基础数学专业,获理学博士学位。1997年7月至1999年6月在南开数学研究所理论物理研究室从事博士后研究,期间于1998年5月至1999年4月作为博士后在韩国汉城的亚太地区理论物理中心(APCTP)工作一年。1999年7月至今在南开数学研究所工作,任副教授、教授。2002年9月至2004年5月获王宽诚教育基金会和陈省身数学研究基金资助访问美国新泽西州立Rutgers大学数学系,期间于2003年4月访问美国麻省理工学院数学系。主要从事李理论和数学物理方面的研究,特别是侧重研究与李理论和数学物理相关的一些代数体系的结构及其应用。先后多次应邀在国际会议上作学术报告,负责留学归国人员科研基金,数学天元基金,国家自然科学基金等研究项目。入选2004年度国家教育部“新世纪优秀人才支持计划”。至2004年底,已发表学术论文30余篇,其中19篇被SCI检索。出版中科院研究生教材1部。讲授课程包括《有限群表示理论》、《紧李群表示理论》等。
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292
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成果数
10
【期刊论文】Further Understanding of Hydrogen Atom: Yangian Approach and Physical Effect
白承铭, Cheng-Ming Bai, Mo-Lin Ge, , and Kang Xue
Journal of Statistical Physics, Vol. 102, Nos. 3/4, 2001,-0001,():
-1年11月30日
By applying the representation theory of Y(sl(2)) to Hydrogen atom (HA) the correct spectrum are re-derived. This indicates the consistence between HA and the Yangian algebraic structure and guarantees that there is democracy between angular momentum L and Yangian current J in the sense of conserved currents. The physical effect of Yangian in HA has been predicted that preserves all the known results for HA, but gives rise to abnormal intensities in the spectrum lines near the free state.
Yangian, hydrogen atom, abnormal Zeeman effect.,
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【期刊论文】The automorphisms of Novikov algebras in low dimensions
白承铭, Chengming Bai, , and Daoji Meng
J. Phys. A: Math. Gen. 36(2003)7715-7731,-0001,():
-1年11月30日
Novikov algebras were introduced in connection with Poisson brackets of hydrodynamic type and Hamiltonian operators in the formal variational calculus. They also correspond to a class of vertex algebras. An automorphism of a Novikov algebra is a linear isomorphism ϕ satisfying ϕ(xy)=ϕ(x)ϕ(y) which keeps the algebraic structure. The set of automorphisms of a Novikov algebra is a Lie group whose Lie algebra is just the Novikov algebra's derivation algebra. The theory of automorphisms plays an important role in the study of Novikov algebras. In this paper, we study the automorphisms of Novikov algebras. We get some results on their properties and classification in low dimensions. These results are fundamental in a certain sense, and they will serve as a guide for further development. Moreover, we apply these results to classify Gel'fand-Dorfman bialgebras and Novikov-Poisson lgebras. These results also can be used to study certain phase spaces and geometric classical r-matrices.
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【期刊论文】On fermionic Novikov algebras
白承铭, Chengming Bai, , Daoji Meng and Liguo He
J. Phys. A: Math. Gen. 35(2002)10053-10063,-0001,():
-1年11月30日
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in formal variational calculus. They are a class of left-symmetric algebras with commutative right multiplication operators, which can be viewed as bosonic. Fermionic Novikov algebras are a class of left-symmetric algebras with anti-commutative right multiplication operators. They correspond to a certain Hamiltonian superoperator in a supervariable. In this paper, we commence a study on fermionic Novikov algebras from the algebraic point of view. We will show that any fermionic Novikov algebra in dimension 3 must be bosonic. Moreover,we give the classification of real fermionicNovikov algebras on fourdimensional nilpotent Lie algebras and some examples in higher dimensions. As a corollary, we obtain kinds of four-dimensional real fermionic Novikov algebras which are not bosonic. All of these examples will serve as a guide for further development including the application in physics.
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【期刊论文】The realization of non-transitive Novikov algebras
白承铭, Chengming Bai, and Daoji Meng
J. Phys. A: Math. Gen. 34(2001)6435-6442,-0001,():
-1年11月30日
Novikov algebras were introduced in connection with hydrodynamic-type Poisson brackets and Hamiltonian operators in the formal variational calculus. We have given a kind of realization of transitive Novikov algebras through the Novikov algebras given by S Gelfand and their compatible infinitesimal deformations in Bai and Meng (2001 J. Phys. A: Math. Gen. 34 3363-72). As a further and continuous study, we extend this realization theory to the nontransitive Novikov algebras in the paper. In two and three dimensions, we find that all non-transitive Novikov algebras also can be realized as the Novikov algebras given by S Gelfand and their compatible infinitesimal deformations. Moreover, they have simpler formulae.
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【期刊论文】On the realization of transitive Novikov algebras
白承铭, Chengming Bai and Daoji Meng
J. Phys. A: Math. Gen. 34(2001)3363-3372,-0001,():
-1年11月30日
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in the formal variational calculus. It is well known that the radical of a finite-dimensional Novikov algebra is transitive. In this paper, we prove that a kind realization of Novikov algebras given by S Gel'fand is transitive and we give a deformation theory of Novikov algebras. In two and three dimensions, we find that all transitive Novikov algebras can be realized as the Novikov algebras given by S Gel'fand and their compatible infinitesimal deformations.
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【期刊论文】The classification of Novikov algebras in low dimensions
白承铭, Chengming Bai and Daoji Meng
J. Phys. A: Math. Gen. 34(2001)1581-1594,-0001,():
-1年11月30日
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in the formal variational calculus. For further our understanding and physical applications, we give a classification of Novikov algebras in dimensions two and three in this paper.
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【期刊论文】A Lie algebraic approach to Novikov algebras
白承铭, Chengming Bai a, c, *, Daoji Meng b
Journal of Geometry and Physics 45(2003)218-230,-0001,():
-1年11月30日
Novikov algebras were introduced in connection with Poisson brackets of hydrodynamic type and Hamiltonian operators in the formal variational calculus. The commutator of a Novikov algebra is a Lie algebra. Thus it is useful to relate the study of Novikov algebras to the theory of Lie algebras. In this paper, we will try to realize Novikov algebras through a Lie algebraic approach. Such a realization could be important in physics and geometry.We find that all transitive Novikov algebras in dimension≤3 can be realized as the Novikov algebras obtained through Lie algebras and their compatible linear (global) deformations.
Novikov algebras, Novikov interior derivation algebras, Linear deformation
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【期刊论文】On the Novikov algebra structures adapted to the automorphism structure of a Lie group
白承铭, Chengming Bai a, c, *, Daoji Meng b
Journal of Geometry and Physics 45(2003)105-115,-0001,():
-1年11月30日
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in the formal variational calculus. The commutator of a Novikov algebra is a Lie algebra in which there exists a special affine structure (connection with zero curvature and torsion) defined by the Novikov algebra. For ensuring the consequences for the group structure, we need consider the more intrinsic connections defined by Novikov algebra structures, that is, the connections which are adapted to the automorphism tructure of a Lie group. The resultant Novikov algebra is called a derivation algebra which satisfies every left multiplication operator is a derivation of its sub-adjacent Lie algebra. In this paper, we commence a study of the Novikov derivation algebras and as a consequence, we can construct Novikov algebras on some 2-solvable Lie algebras.
Novikov algebras, Novikov derivation algebras
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【期刊论文】Left-symmetric algebras from linear functions
白承铭, Chengming Bai
Journal of Algebra 281(2004)651-665,-0001,():
-1年11月30日
In this paper, some left-symmetric algebras are constructed from linear functions. They include a kind of simple left-symmetric algebras and some examples appearing in mathematical physics. Their complete classification is also given, which shows that they can be regarded as generalization of certain two-dimensional left-symmetric algebras.
Left-symmetric algebra, Linear function, Lie algebra
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【期刊论文】HAPPER'S CURIOUS DEGENERACIES AND YANGIAN
白承铭, CHENG-MING BAI, MO-LIN GE, KANG XUE,
International Journal of Modern Physics B, Vol. 16, Nos. 14 & 15(2002)1867-1873,-0001,():
-1年11月30日
We find raising and lowering operators distinguishing the degenerate states for the Hamiltonian H=x(K+12)Sz+K•S at x=1 for spin 1 that was given by Happer et al.1, 2 to interpret the curious degeneracies of the Zeeman e ect for condensed vapor of 87Rb. The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of Y (sl(2)).
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