Related papers: Powers of Elements in Jordan Loops

Isotopes of C-loops with unique non-identity squares are shown to be both C-loops and A-loops. The relationship between C-loops and Steiner loops is further studied. Central loops with the weak and cross inverse properties are also…

Recently J.A.Anquela, T.Cort\'es, and H.Petersson proved that for elements $x, y$ in a non-degenerate Jordan algebra $J$, the relation $x \circ y = 0$ implies that the $U$-operators of $x$ and $y$ commute: $U_xU_y = U_yU_x$. We show that…

Triangular matrix rings are example of trivial extensions. In this article we describe the Jordan superderivations of the trivial extensions and upper triangular matrix rings. We deduce then that any Jordan superderivation of an upper…

We investigate relations between the properties of an algebra and its varieties of finite-dimensional module structures, on the example of the Jordan plane $R=k<x,y>/ (xy-yx-y^2)$. Complete description of irreducible components of the…

It is well-known that a nilpotent n by n matrix B is determined up to conjugacy by a partition of n formed by the sizes of the Jordan blocks of B. We call this partition the Jordan type of B. We obtain partial results on the following…

In this article, a new notion of $n$-Jordan homomorphism namely the mixed $n$-Jordan homomorphism is introduced. It is proved that how a mixed $(n+1)$-Jordan homomorphism can be a mixed $n$-Jordan homomorphism and vice versa. By means of…

In this paper, we classify Jordan superalgebras of dimension up to three over an algebraically closed field of characteristic different of two. Our main motivation to obtain such classification comes out from the intention to give an answer…

In this paper, we investigate metric Jordan algebras, and follow the lines of the paper (J. Milnor: Curvatures of left invariant metrics on Lie groups. Adv. Math. (1976)). Firstly, we define the Jordan-Levi-Civita connection, then we show…

We prove a non-associative analog to the well-known $\frac{5}{8}$ Theorem. Namely, for a finite Moufang loop with nuclear commutators, we show that if the probability that three randomly chosen elements associate is greater than…

We present a construction of a Jordan scheme from an elementary abelian $2$-group of rank $n$ and a $\{1,-1\}$-matrix of order $2^n$ that satisfies a specified condition. We then prove that the orders of matrices with the specified…

Nonrelativistic quantum mechanics and conformal quantum mechanics are deformed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian…

Jordan as well as related triple systems have been used to find several solutions of the Yang-Baxter equation, which are of rational as well as trigonometric type.

The dynamics of all quadratic Newton maps of rational functions are completely described. The Julia set of such a map is found to be either a Jordan curve or totally disconnected. It is proved that no Newton map with degree at least three…

Automorphic loops are loops in which all inner mappings are automorphisms. This variety of loops includes, for instance, groups and commutative Moufang loops. We study uniquely 2-divisible automorphic loops, particularly automorphic loops…

Let $Q$ be a quiver of $A_n$ type and $\mathbb{K}$ be an algebraically closed field. A nilpotent endomorphism of a quiver representation induces a linear transformation of the vector space at each vertex. Generically among all nilpotent…

A new matrix model is described, based on the exceptional Jordan algebra. The action is cubic, as in matrix Chern-Simons theory. We describe a compactification that, we argue, reproduces, at the one loop level, an octonionic…

Let $A$ be a unital algebra over a field $F$ with $\operatorname*{char} (F)\neq2$. In this paper we introduce a new concept of a generalized Jordan derivation, covering Jordan centralizers and Jordan derivations, as follows: a linear map…

Using Bessel-Muirhead system, we can express the K-bessel function defined on a Jordan algebra as linear combination of the J-solutions. We determine explicitly the coefficients when the rank of this Jordan algebra is three after a…

In positive characteristic the Jordan plane covers a finite-dimensional Nichols algebra that was described by Cibils, Lauve and Witherspoon and we call the restricted Jordan plane. In this paper the characteristic is odd. The defining…

Relative positional encodings determine which functions of query-key lag can enter the primitive attention logit. RoPE supplies a rotary phase, while ALiBi supplies an additive distance bias. Motivated by group-theoretic views of linear…