Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions

Higher Polynomial Identities for Mutations of Associative Algebras

“…A linear basis of corresponds to (the cosets of) the rows of whose leading 1 s have column indices in . It is straightforward using the module generators algorithm [ 4 ] to compute a subset of this linear basis which represents a set of -module generators for the quotient module. Computations with the computer algebra system SageMath show that and hence has rank ; the nonzero entries of are .…”

“… Linear algebra over the integers: the Hermite normal form of a matrix and the Lenstra–Lenstra–Lovász algorithm (LLL, see [ 5 , 9 ]) for lattice basis reduction. We consider only multilinear identities for the original operation : this allows us to use the representation theory of the symmetric group [ 4 ] to decompose the computations into small pieces corresponding to irreducible representations. …”

“…We consider only multilinear identities for the original operation : this allows us to use the representation theory of the symmetric group [ 4 ] to decompose the computations into small pieces corresponding to irreducible representations.…”