arXiv subjects

Alexander Pozhidaev

Publications and source records attributed to Alexander Pozhidaev.

2 recordsLinked to original sources

arXiv2018

Rota-Baxter Operators on Quadratic Algebras

We prove that all Rota-Baxter operators on a quadratic division algebra are trivial. For nonzero weight, we state that all Rota-Baxter operators on the simple odd-dimensional Jordan algebra of bilinear form are projections on a subalgebra along another one. For weight zero, we find a connection between the Rota-Baxter operators and the solutions to the alternative Yang-Baxter equation on the Cayley-Dickson algebra. We also investigate the Rota-Baxter operators on the matrix algebras of order two, the Grassmann algebra of plane, and the Kaplansky superalgebra.

math.RA↗

arXiv2017

On a ternary generalization of Jordan algebras

Based on the relation between the notions of Lie triple systems and Jordan algebras, we introduce the $n$-ary Jordan algebras,an $n$-ary generalization of Jordan algebras obtained via the generalization of the following property $\left[ R_{x},R_{y}\right] \in Der\left( \mathcal{A}\right)$, where $\mathcal{A}$ is an $n$-ary algebra. Next, we study a ternary example of these algebras. Finally, based on the construction of a family of ternary algebras defined by means of the Cayley-Dickson algebras, we present an example of a ternary $D_{x,y}$-derivation algebra ($n$-ary $D_{x,y}$-derivation algebras are the non-commutative version of $n$-ary Jordan algebras).

math.RA↗