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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】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】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 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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