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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】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】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】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】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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