One-generated nilpotent bicommutative algebras
We give a classification of $5$- and $6$-dimensional complex one-generated nilpotent bicommutative algebras.
math.RA↗
arXiv subjects
Vasily Voronin
Publications and source records attributed to Vasily Voronin.
The algebraic and geometric classification of nilpotent bicommutative algebras
We classify the $4$-dimensional nilpotent bicommutative algebras over $\mathbb C$ from both algebraic and geometric approaches.
math.RA↗
Special and exceptional Jordan dialgebras
In this paper, we study the class of Jordan dialgebras. We develop an approach for reducing problems on dialgebras to the case of ordinary algebras. It is shown that straightforward generalizations of the classical Cohn's, Shirshov's, and Macdonald's Theorems do not hold for dialgebras. However, we prove dialgebraic analogues of these statements. Also, we study polylinear special identities which hold in all special Jordan algebras and do not hold in all Jordan algebras. We find a natural correspondence between special identities for ordinary algebras and dialgebras.
math.RA↗