Related papers: Novikov algebras and multi-indices in regularity s…
Firstly, we introduce a notion of anti-pre-Novikov algebras as a new framework for decomposing Novikov algebras. Anti-O-operators on Novikov algebras are developed to provide an algebraic framework for constructing anti-pre-Novikov…
We describe a method for classifying the Novikov algebras with a given associated Lie algebra. Subsequently we give the classification of the Novikov algebras of dimension 3 over R and C, as well as the classification of the 4-dimensional…
Pre-Novikov algebras and quasi-Frobenius Novikov algebras naturally appear in the theory of Novikov bialgebras. In this paper, we show that there is a natural pre-Novikov algebra structure associated to a quasi-Frobenius Novikov algebra.…
We introduce higher-order (or multibracket) simple Lie algebras that generalize the ordinary Lie algebras. Their `structure constants' are given by Lie algebra cohomology cocycles which, by virtue of being such, satisfy a suitable…
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 introduce a hierarchy of degree structures between the Medvedev and Muchnik lattices which allow varying amounts of non-uniformity. We use these structures to introduce the notion of the uniformity of a Muchnik reduction, which expresses…
An algebra with identities $a\circ(b\circ c-c\circ b)=(a\circ b)\circ c-(a\circ c)\circ b$ and $a\circ(b\circ c)=b\circ(a\circ c)$ is called Novikov. We construct free Novikov base in terms of Young diagrams. We show that codimensions…
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 describe arithmetic computations in terms of operations on some well known free algebras (S1S, S2S and ordered rooted binary trees) while emphasizing the common structure present in all them when seen as isomorphic with the set of…
In this paper, we consider Novikov algebra with derivation and algebra obtained from its dual operad. It turns out that the obtained dual operad has a connection with bicommutative algebras. The motivation for this work comes from the white…
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,…
This paper is devoted to the complete algebraic classification of complex $5$-dimensional nilpotent Novikov algebras.
In this paper, we study Novikov algebras satisfying nontrivial identities. We show that a Novikov algebra over a field of zero characteristic that satisfies a nontrivial identity satisfies some unexpected "universal" identities, in…
Algebras with identity $(a\star b)\star (c\star d) -(a\star d)\star(c\star b)$ $=(a,b,c)\star d-(a,d,c)\star b$ are studied. Novikov algebras under Jordan multiplication and Leibniz dual algebras satisfy this identity. If algebra with such…
The results from the article [Strachan I.A.B., Szablikowski B.M., Stud. Appl. Math. 133 (2014), 84-117] are extended over consideration of central extensions allowing the introducing of additional independent variables. Algebraic conditions…
We introduce a modified version of the necklace Lie bialgebra associated to a quiver, in which the bracket and cobracket insert (rather than remove) pairs of arrows in involution. This structure is then related to canonical quartic…
We use the diagram-free approach to regularity structures introduced by Otto et. al. to build rough paths based on multi-indices. We identify the analogue of the insertion pre-Lie algebra of trees and use it to build the corresponding group…
Recent advances in stochastic PDEs, Hopf algebras of typed trees and integral equations have inspired the study of algebraic structures with replicating operations. To understand their algebraic and combinatorial nature, we first use rooted…
This paper is devoted to give the complete algebraic and geometric classification of $4$-dimensional nilpotent Novikov algebras over $\mathbb C.$
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…