19 citations · 201 across the 54 of their papers we have counts for
10 papers · 1 filter
The fundamental invariants of 3 x 3 x 3 arrays
Murray R. Bremner, Jiaxiong Hu
We determine the three fundamental invariants in the entries of a array over as explicit polynomials in the 27 variables for $1 \le i,…
Ranks of 0-1 arrays of size 2 x 2 x 2 and 2 x 2 x 2 x 2
Murray R. Bremner, Stavros G. Stavrou
We use computer algebra to determine the ranks of arrays of size 2 x 2 x 2 and 2 x 2 x 2 x 2 with entries in the set {0, 1} regarded as a field with two elements, as a Boolean alge…
The hyperdeterminant of 3 x 3 x 2 arrays, and the simplest invariant of 4 x 4 x 2 arrays
Murray R. Bremner
We use the representation theory of Lie algebras and computational linear algebra to obtain an explicit formula for the hyperdeterminant of a array: a homogen…
Polynomial identities for tangent algebras of monoassociative loops
Murray R. Bremner, Sara Madariaga
We introduce degree n Sabinin algebras, which are defined by the polynomial identities up to degree n in a Sabinin algebra. Degree 4 Sabinin algebras can be characterized by the po…
The simple non-Lie Malcev algebra as a Lie-Yamaguti algebra
Murray R. Bremner, Andrew Douglas
The simple 7-dimensional Malcev algebra is isomorphic to the irreducible -module V(6) with binary product defined by the $\…
Malcev dialgebras
Murray R. Bremner, Luiz A. Peresi, Juana Sanchez-Ortega
We apply Kolesnikov's algorithm to obtain a variety of nonassociative algebras defined by right anticommutativity and a `noncommutative' version of the Malcev identity. We use comp…