Related papers: Relative (pre-)anti-flexible algebras and associat…
We introduce the notion of quasi-triangular Novikov bialgebras, which constructed from solutions of the Novikov Yang-Baxter equation whose symmetric parts are invariant. Triangular Novikov bialgebras and factorizable Novikov bialgebras are…
We study possibilities for algebraic closures, differences between definable and algebraic closures in first-order structures, and variations of these closures with respect to the bounds of cardinalities of definable sets and given sets of…
We develop the bialgebra theory for two classes of non-associative algebras: nearly associative algebras and $LR$-algebras. In particular, building on recent studies that reveal connections between these algebraic structures, we establish…
In this paper, we introduce the cohomology theory of relative Rota-Baxter operators on Leibniz triple systems. We use the cohomological approach to study linear and formal deformations of relative Rota-Baxter operators. In particular,…
Representations of Hom-Jacobi-Jordan algebras are studied. In particular, adjoint representations and trivial representations are studied in detail. Derivations and central extensions of Hom-Jacobi-Jordan algebras are also discussed as an…
Weighted Rota-Baxter Jacobi-Jordan algebras and their representations are studied. Moreover, we consider weighted Rota-Baxter paired operators that are related to weighted Rota-Baxter Jacobi-Jordan algebras together with their…
The PostLie algebra is an enriched structure of the Lie algebra that has recently arisen from operadic study. It is closely related to pre-Lie algebra, Rota-Baxter algebra, dendriform trialgebra, modified classical Yang-Baxter equations and…
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.…
This paper introduces Hopf braces, a new algebraic structure related to the Yang-Baxter equation which include Rump's braces and their non-commutative generalizations as particular cases. Several results of classical braces are still valid…
The main purpose of this work is to develop the basic notions of the Lie theory for commutative algebras. We introduce a class of $\mathbbZ_2$-graded commutative but not associative algebras that we call ``Lie antialgebras''. These algebras…
A Baxter algebra is a commutative algebra $A$ that carries a generalized integral operator. In the first part of this paper we review past work of Baxter, Miller, Rota and Cartier in this area and explain more recent work on explicit…
In this paper we generalize cellular algebras by allowing different partial orderings relative to fixed idempotents. For these relative cellular algebras we classify and construct simple modules, and we obtain other characterizations in…
The notions of left-right noncommutative Poisson algebra ($\NP^{lr}$-algebra) and left-right algebra with bracket $\AWB^{lr}$ are introduced. These algebras are special cases of $\NLP$-algebras and algebras with bracket $\AWB$,…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
Reductions for systems of ODEs integrable via the standard factorization method (the Adler-Kostant-Symes scheme) or the generalized factorization method, developed by the authors earlier, are considered. Relationships between such…
We determine normal forms of the multiplication of four-dimensional anti-commutative algebras over a field $\mathbb K$ of characteristic zero having an analogous family of flags of subalgebras as the four-dimensional non-Lie binary Lie…
We associate elliptic affine Lie algebras with what are called vertex $\C((z))$-algebras and their modules in a certain category. In the course, we construct two families of Lie algebras closely related to elliptic affine Lie algebras.
We equip a matrix algebra with a weighted infinitesimal unitary bialgebraic structure, via a construction of a suitable coproduct. Furthermore, an infinitesimal unitary Hopf algebra, under the view of Aguiar, is constructed on a matrix…
We generalize the classical study of (generalized) Lax pairs and the related $O$-operators and the (modified) classical Yang-Baxter equation by introducing the concepts of nonabelian generalized Lax pairs, extended $\calo$-operators and the…
This paper examines whether the concept of an almost-algebraic Lie algebra developed by Auslander and Brezin in \cite{ab} can be introduced for Leibniz algebras. Two possible analogues are considered: almost-reductive and almost-algebraic…