Читать книгу Algebra and Applications 2 - Группа авторов - Страница 48

A Novikov algebra is a right pre-Lie algebra which is also left NAP, namely, a vector space A together with a bilinear product ∗, such that, for any a, b, c ∈ A, we have:

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Novikov algebras first appeared in hydrodynamical equations (Balinskii and Novikov 1985; Osborn 1992). The prototype is a commutative associative algebra together with a derivation D, with the Novikov product being given by:

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The free Novikov algebra on a set of generators has been given in Dzhumadil’daev and Löfwall (2002, section 7) in terms of some classes of rooted trees.