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arXiv · 1907.01706

Semi-Associative $3$-Algebras

Ruipu Bai·Yan Zhang
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Abstract

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 $(ϕ, ψ, M)$ and a cocycle $θ$, a semi-direct product semi-associative $3$-algebra $A\ltimes_{ϕψ} M $ and a double extension $(A\dot+A^*, \{ , , \}_θ)$ are constructed, and structures are studied.

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Ruipu Bai, Yan Zhang. 2019-07-03. Semi-Associative $3$-Algebras. https://arxiv.org/abs/1907.01706

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