Year: 2019
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Bai, Ruipu, Zhang, Yan
Institution: Hebei University
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2954867202