Higher identities for the ternary commutator

We use computer algebra to study polynomial identities for the trilinear operation [a, b, c] = abc − acb − bac + bca + cab − cba in the free associative algebra. It is known that [a, b, c] satisfies the alternating property in degree 3, no new identities in degree 5, a multilinear identity in degree...

Full description

Saved in:
Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-12, Vol.45 (50), p.505201-12
Main Authors: Bremner, M R, Peresi, L A
Format: Article
Language:English
Subjects:
Algebra
C (programming language)
Commutators
Computer algebra
Exact sciences and technology
Lie algebras
Mathematical models
Partitions
Permutations
Physics
polynomial identities
Polynomials
representation theory
Representations
ternary commutator
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We use computer algebra to study polynomial identities for the trilinear operation [a, b, c] = abc − acb − bac + bca + cab − cba in the free associative algebra. It is known that [a, b, c] satisfies the alternating property in degree 3, no new identities in degree 5, a multilinear identity in degree 7 which alternates in 6 arguments, and no new identities in degree 9. We use the representation theory of the symmetric group to demonstrate the existence of new identities in degree 11. The only irreducible representations of dimension
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/50/505201