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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 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】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】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】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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