Vidinli algebras

TL;DR

This paper introduces Vidinli algebras, a new class of nonassociative algebras characterized by a scalar multiple commutator, generalizing Jordan algebras of Clifford type and expanding in characteristic 2.

Contribution

It defines Vidinli algebras and explores their properties, including their relation to existing algebra classes and their behavior in different characteristics.

Findings

Vidinli algebras generalize Jordan algebras of Clifford type.

In characteristic 2, they include unitizations of anticommutative algebras.

They are conic (quadratic) algebras with scalar multiple commutators.

Abstract

A new class of nonassociative algebras, Vidinli algebras, is defined based on recent work of Co\c{s}kun and Eden. These algebras are conic (or quadratic) algebras with the extra restriction that the commutator of any two elements is a scalar multiple of the unity. Over fields of characteristic not 2, Vidinli algebras may be considered as generalizations of the Jordan algebras of Clifford type. However, in characteristic 2, the class of Vidinli algebras is much larger and include the unitizations of anticommutative algebras.