Abstract:We study Lie brackets and Jordan products derived from associative opera-We use computational linear algebra, based on the representation theory of the symmetric group, to determine all polynomial identities of degree ≤ 7 relating (i) the two Lie brackets, (ii) one Lie bracket and one Jordan product, and (iii) the two Jordan products. For the Lie-Lie case, there are two new identities in degree 6 and another two in degree 7. For the Lie-Jordan case, there are no new identities in degree ≤ 6 and a complex set o… Show more
“…The calculations are similar to those discussed in detail in previous sections, so we provide only a brief outline. The number of distinct association types in arity n for two commutative operations is sequence OEIS A226909; see also [10]:…”
“…The calculations are similar to those discussed in detail in previous sections, so we provide only a brief outline. The number of distinct association types in arity n for two commutative operations is sequence OEIS A226909; see also [10]:…”
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.