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On the Novikov algebra structures adapted to the automorphism structure of a Lie group

✍ Scribed by Chengming Bai; Daoji Meng

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 81 KB
Volume: 45
Category: Article
ISSN: 0393-0440
DOI: 10.1016/s0393-0440(02)00127-4

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✦ Synopsis

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 structure 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.

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