Mutation algebras of a nonassociative algebra

Higher polynomial identities for mutations of associative algebras

“…We apply all permutations in S 3 to the arguments a, b, c in the equations (1), and store the coefficients of the monomials in the 24 × 12 matrix E 3 representing X 3 with respect to the ordered bases (Figure 2). That is, the (i, j) entry of E 3 is the coefficient of the i-th associative monomial (3) in the expansion of the j-th nonassociative monomial (2). It is easy to check that this matrix has rank 11 and hence nullity 1, and that a basis for its nullspace is the coefficient vector of the Lie-admissible identity.…”

“…For each row of N 4 , we multiply the coefficients by the LCM of their denominators to obtain integers and then divide by the GCD of these integer coefficients. The squared Euclidean lengths of the resulting vectors with multiplicities in parentheses are 12(4), 18(4), 42(8), 48(2), 56(1), 60(4), 64(1), 72(2), 74(3), 82(1), 100 (2).…”

“…For a detailed exposition of the structure theory of mutation algebras, see [6]. For mutations of nonassociative algebras, see [2].…”

Higher Polynomial Identities for Mutations of Associative Algebras

“…For a detailed exposition of the structure theory of mutation algebras, see [ 6 ]. For mutations of nonassociative algebras, see [ 2 ].…”