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On a pre-Jacobi-Jordan algebra: relevant properties and double construction (2007.06736v1)
Published 13 Jul 2020 in math.RA
Abstract: We introduce a pre-Jacobi-Jordan algebras and study some relevant properties such as bimodules, matched pairs. Besides, we established a pre-Jacobi-Jordan algebra built as a direct sum of a given pre-Jacobi-Jordan algebra $(\A, \cdot)$ and its dual $(\A{\ast}, \circ),$ endowed with a non-degenerate symmetric bilinear form $B,$ where $\cdot$ and $\circ$ are the products defined on $\A$ and $\A{\ast},$ respectively. Finally, after pre-Jacobi-Jordan algebras classification in dimension two, we thoroughly give some double constructions of pre-Jacobi-Jordan algebraic structures.