A double construction of quadratic anticenter-symmetric Jacobi-Jordan algebras

Abstract

This work addresses some relevant characteristics and properties of anticenter-symmetric Jacobi-Jordan algebras such as bimodules, matched pairs. Besides, the Jacobi-Jordan admissible algebra is defined; a special emphasis is given to a double construction of quadratic anticenter-symmetric algebras. We then follow this theory with the main properties and related algebraic structures of an anticenter-symmetric JJ algebra, namely the anti-Zinbiel algebras. Finally, we discuss the double construction of some classes of the two dimensional anticenter-symmetric JJ algebras.