• 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}
}
• 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 $(A\dot+A… ## References SHOWING 1-10 OF 10 REFERENCES • Mathematics • 2009 The notion of$n$-ary algebras, that is vector spaces with a multiplication concerning$n$-arguments,$n \geq 3\$, became fundamental since the works of Nambu. Here we first present general notions
• Mathematics
• 2012
AbstractWe study the structure of a metric n-Lie algebra $$\mathcal{G}$$ over the complex field ℂ. Let $$\mathcal{G} = \mathcal{S} \oplus \mathcal{R}$$ be the Levi decomposition, where
• Mathematics
Advances in Theoretical and Mathematical Physics
• 2019
This paper studies two types of 3-Lie bialgebras whose compatibility conditions between the multiplication and comultiplication are given by local cocycles and double constructions respectively, and
• Mathematics
• 2010
3-Lie algebras have close relationships with many important fields in mathematics and mathematical physics. In this paper, we provide a construction of 3-Lie algebras in terms of Lie algebras and
• Mathematics, Physics
• 2008
In previous work we proposed a field theory model for multiple M2-branes based on an algebra with a totally antisymmetric triple product. In this paper we gauge a symmetry that arises from the

• 2007

### On foundation of the genneralized Nambu mechanics

• Communications in Mathematical Physics
• 1994

### N.Lambert, Modeling Multiple M2S

• Physical Review,
• 2007

### On decomposability of Nambu-Poission tensor

• Acta Mathematica Universitatis Comenianae
• 1996