相关论文: Z_n Quasialgebras

In this paper we introduce the theory of multiplication alteration by two-cocycles for nonassociative structures like nonassociative bimonoids with left (right) division. Also we explore the connections between Yetter-Drinfeld modules for…

We describe all the quasi-bialgebra structures of a group algebra over a torsion-free abelian group. They all come out to be triangular in a unique way. Moreover, up to an isomorphism, these quasi-bialgebra structures produce only one…

Motivated by M-theory, we define a new type of non-associative algebra involving usual and cubic matrices at the same time. The resulting algebra can be regarded as a two-term truncated $L_\infty$ algebra giving rise to a fundamental…

We present a survey of recent results, scattered in a series of papers that appeared during past five years, whose common denominator is the use of cubic relations in various algebraic structures. Cubic (or ternary) relations can represent…

The nontrivial unital composition superalgebras, of dimension 3 and 6, which exist only in characteristic 3, are obtained from the split Cayley algebra and its order 3 automorphisms, by means of the process of semisimplification of the…

A general notion of a quasi-finite algebra is introduced as an algebra graded by the set of all integers equipped with topologies on the homogeneous subspaces satisfying certain properties. An analogue of the regular bimodule is introduced…

For an arbitrary octonion algebra, we determine all subalgebras. It turns out that every subalgebra of dimension less than four is associative, while every subalgebra of dimension greater than four is not associative. In any split octonion…

We provide a description of the class of n-ary operations on an arbitrary chain that are quasitrivial, symmetric, nondecreasing, and associative. We also prove that associativity can be replaced with bisymmetry in the definition of this…

It is known that there are Lie algebras with non-semigroup gradings, i.e. such that the binary operation on the grading set is not associative. We provide a similar example in the class of associative algebras.

Octonion algebras are certain algebras with a multiplicative quadratic form. In their 2019 article, Alsaody and Gille show that, for octonion algebras over unital commutative rings, there is an equivalence between isotopes and isometric…

Quasifolds are singular spaces that generalize manifolds and orbifolds. They are locally modeled by manifolds modulo the smooth action of countable groups and they are typically not Hausdorff. If the countable groups happen to be all…

This paper is a sequel to arXiv:2307.13358 and arXiv:2308.16090. A construction associating a semialgebra with an algebra, subalgebra, and a coalgebra dual to the subalgebra played a central role in the author's book arXiv:0708.3398. In…

Biserial algebras are a classical class in the representation theory of algebras, generalizing Nakayama algebras. They were further generalized by Green and Schroll to multiserial algebras, which share many structural properties with…

Following the analogy between algebras (monoids) and monoidal categories the construction of nucleus for non-associative algebras is simulated on the categorical level. Nuclei of categories of modules are considered as an example.

Let $H$ be a quasitriangular quasi-Hopf algebra, we construct a braided group $\underline{H}$ in the quasiassociative category of left $H$-modules. Conversely, given any braided group $B$ in this category, we construct a quasi-Hopf algebra…

We investigate the notion of associated graded coalgebra (algebra) of a bialgebra with respect to a subbialgebra (quotient bialgebra) and characterize those which are bialgebras of type one in the framework of abelian braided monoidal…

It is known that semigroups are Ramsey algebras. This paper is an attempt to understand the role associativity plays in a binary system being a Ramsey algebra. Specifically, we show that the nonassociative Moufang loop of octonions is not a…

We introduce a new type of noncommutative Poisson structure on associative algebras. It induces Poisson structures on the moduli spaces classifying semisimple modules. Path algebras of doubled quivers and preprojective algebras have…

Motivated by the theory of quasi-determinants, we study non-commutative algebras of quasi-Pl\"ucker coordinates. We prove that these algebras provide new examples of non-homogeneous quadratic Koszul algebras by showing that their quadratic…

Many quantum groups and quantum spaces of interest can be obtained by cochain (but not cocycle) twist from their corresponding classical object. This failure of the cocycle condition implies a hidden nonassociativity in the noncommutative…