• Corpus ID: 195791713

Semi-Associative $3$-Algebras

@article{Bai2019SemiAssociative,
  title={Semi-Associative \$3\$-Algebras},
  author={Ruipu Bai and Yan Zhang},
  journal={arXiv: Mathematical Physics},
  year={2019}
}

• R. Bai, Yan Zhang
• Published 3 July 2019
• Mathematics
• arXiv: Mathematical Physics

A new 3-ary non-associative algebra, which is called a semi-associative $3$-algebra, is introduced, and the double modules and double extensions by cocycles are provided. Every semi-associative $3$-algebra $(A, \{ , , \})$ has an adjacent 3-Lie algebra $(A, [ , , ]_c)$. From a semi-associative $3$-algebra $(A, \{, , \})$, a double module $(\phi, \psi, M)$ and a cocycle $\theta$, a semi-direct product semi-associative $3$-algebra $A\ltimes_{\phi\psi} M $ and a double extension $(A\dot+A^*, \{ , , \}_{\theta})$ are constructed, and structures are studied.