Related papers: General multi-Novikov algebras, multi-differential…
In this work, we introduce multi-Novikov algebras, a generalisation of Novikov algebras with several binary operations indexed by a given set, and show that the multi-indices recently introduced in the context of singular stochastic partial…
As it is known, the defining identities of a free Novikov algebra can be obtained from a commutative algebra with a derivation. In this paper, we consider a class of algebras obtained from the class of associative algebras with a derivation…
The class of Novikov algebras is a popular object of study among classical nonassociative algebras. The generic example of a Novikov algebra may be obtained from a differential associative and commutative algebra. We consider a more general…
This article considers the structure and properties of $\delta$-Novikov algebras, a generalization of Novikov algebras characterized by a scalar parameter $\delta$. It looks like $\delta$-Novikov algebras have a richer structure than…
A Gelfand-Dorfman algebra is called special if it can be embedded into a differential Poisson algebra. We find a new basis of the free Novikov algebra. With its help, we construct the monomial basis of the free special Gelfand-Dorfman…
It is shown that the variety of transposed Poisson algebras coincides with the variety of Gelfand-Dorfman algebras in which the Novikov multiplication is commutative. The Gr\"obner-Shirshov basis for the transposed Poisson operad is…
Novikov algebras are algebras whose associators are left-symmetric and right multiplication operators are mutually commutative. A Gel'fand-Dorfman bialgebra is a vector space with a Lie algebra structure and a Novikov algebra structure,…
A method for the construction of classes of examples of multi-dimensional, multi-component Dubrovin-Novikov brackets of hydrodynamic type is given. This is based on an extension of the original construction of Gelfand and Dorfman which gave…
The notion of $\delta$-Novikov algebras was introduced recently as a generalization of Novikov and bicommutative algebras. It looks like $\delta$-Novikov algebras have a richer structure than Novikov algebras. So, unlike Novikov algebras,…
Generalizing S. Gelfand's classical construction of a Novikov algebra from a commutative differential algebra, a deformation family $(A,\circ_q)$, for scalars $q$, of Novikov algebras is constructed from what we call an admissible…
We propose a combinatorial formula for the coproduct in a Hopf algebra of decorated multi-indices that recently appeared in the literature, which can be briefly described as the graded dual of the enveloping algebra of the free Novikov…
We study a twisted generalization of Novikov algebras, called Hom-Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom-Novikov algebras can be obtained from Novikov algebras by twisting…
We study polynomial Poisson algebras with some regularity conditions. Linear (Lie-Berezin-Kirillov) structures on dual spaces of semi-simple Lie algebras, quadratic Sklyanin elliptic algebras of \cite{FO1},\cite{FO2} as well as polynomial…
Polynomial identities of two-dimensional Novikov algebras are studied over the complex field $\mathbb{C}$. We determine minimal generating sets for the T-ideals of the polynomial identities and linear bases for the corresponding relatively…
A Novikov conformal algebra is a conformal algebra such that its coefficient algebra is right-symmetric and left commutative (i.e., it is an ``ordinary'' Novikov algebra). We prove that every Novikov conformal algebra with a uniformly…
We provide a general notion of induced structures of operated algebras in the context of unary-binary operads. This notion fully captures the binary quadratic relations encoded by a unary-binary operad, thereby unifying and formalizing the…
This paper first develops a bialgebra theory for a noncommutative Novikov algebra, called a noncommutative Novikov bialgebra, which is further characterized by matched pairs and Manin triples of noncommutative Novikov algebras. The…
In this paper, we introduce the definition of transposed Novikov-Poisson algebras, whose affinization are transposed Poisson algebras. Moreover, we show that there is a natural transposed Poisson algebra structure on the tensor product of a…
We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures, and investigate the relations between them. A commutative Hopf algebra of permutations is obtained by a general…
The notions of the Novikov deformation of a commutative associative algebra and the corresponding classical limit are introduced. We show such a classical limit belongs to a subclass of transposed Poisson algebras, and hence the Novikov…