0-dialgebras with bar-unity and nonassociative Rota--Baxter algebras.
A -grading on a -dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type
We describe two constructions of a certain -grading on the so-called Brown algebra (a simple structurable algebra of dimension and skew-dimension ) over an algebraically closed field of characteristic different from . The Weyl group of this grading is computed. We also show how this grading gives rise to several interesting fine gradings on exceptional simple Lie algebras of types , and .
A class of fermionic Novikov superalgebras which is a class of Novikov superalgebras
We construct a special class of fermionic Novikov superalgebras from linear functions. We show that they are Novikov superalgebras. Then we give a complete classification of them, among which there are some non-associative examples. This method leads to several new examples which have not been described in the literature.
A Class of Nonassociative Algebras with Involution Containing the Class of Jordan Algebras.
A new approach to Hom-left-symmetric bialgebras
The main purpose of this paper is to consider a new definition of Hom-left-symmetric bialgebra. The coboundary Hom-left-symmetric bialgebra is also studied. In particular, we give a necessary and sufficient condition that -matrix is a solution of the Hom--equation by a cocycle condition.
A note on commutativity of nonassociative rings.
A review on δ-structurable algebras
In this paper we give a review on δ-structurable algebras. A connection between Malcev algebras and a generalization of δ-structurable algebras is also given.
A simple symmetry generating operads related to rooted planar -ary trees and polygonal numbers.
Affine endomorphism near-rings
Basis for identities of the algebra of simplified insertion.
Classification of 4-dimensional nilpotent complex Leibniz algebras.
(Co)homology of triassociative algebras.
Conservative algebras and superalgebras: a survey
We give a survey of results obtained on the class of conservative algebras and superalgebras, as well as on their important subvarieties, such as terminal algebras.
Construction of Nijenhuis operators and dendriform trialgebras.
Contributions to the theory of (1,1) rings
Embedding of dendriform algebras into Rota-Baxter algebras
Following a recent work [Bai C., Bellier O., Guo L., Ni X., Splitting of operations, Manin products, and Rota-Baxter operators, Int. Math. Res. Not. IMRN (in press), DOI: 10.1093/imrn/rnr266] we define what is a dendriform dior trialgebra corresponding to an arbitrary variety Var of binary algebras (associative, commutative, Poisson, etc.). We call such algebras di- or tri-Var-dendriform algebras, respectively. We prove in general that the operad governing the variety of di- or tri-Var-dendriform...
Fermionic Novikov algebras admitting invariant non-degenerate symmetric bilinear forms
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in the formal variational calculus. Fermionic Novikov algebras correspond to a certain Hamiltonian superoperator in a supervariable. In this paper, we show that fermionic Novikov algebras equipped with invariant non-degenerate symmetric bilinear forms are Novikov algebras.
Finite-dimensional Left Moufang Algebras.
F-quasigroups and generalized modules
In Kepka T., Kinyon M.K., Phillips J.D., The structure of F-quasigroups, J. Algebra 317 (2007), 435–461, we showed that every F-quasigroup is linear over a special kind of Moufang loop called an NK-loop. Here we extend this relationship by showing an equivalence between the class of (pointed) F-quasigroups and the class corresponding to a certain notion of generalized module (with noncommutative, nonassociative addition) for an associative ring.
F-quasigroups isotopic to groups
In Kepka T., Kinyon M.K., Phillips J.D., The structure of F-quasigroups, math.GR/0510298, we showed that every loop isotopic to an F-quasigroup is a Moufang loop. Here we characterize, via two simple identities, the class of F-quasigroups which are isotopic to groups. We call these quasigroups FG-quasigroups. We show that FG-quasigroups are linear over groups. We then use this fact to describe their structure. This gives us, for instance, a complete description of the simple FG-quasigroups. Finally,...