19 citations · 74 across the 13 of their papers we have counts for
13 papers
Jordan Trialgebras and Post-Jordan Algebras
Fatemeh Bagherzadeh, Murray Bremner, Sara Madariaga
We compute minimal sets of generators for the S_n-modules (n <= 4) of multilinear polynomial identities of arity n satisfied by the Jordan product and the Jordan diproduct (resp. p…
Linear representations of formal loops
S. Madariaga, José M. Pérez-Izquierdo
A representation of an object in a category is an abelian group in the corresponding comma category. In this paper we derive the formulas describing linear representations of objec…
Lie and Jordan products in interchange algebras
Murray Bremner, Sara Madariaga
We study Lie brackets and Jordan products derived from associative operations satisfying the interchange identity $(w \bullet x ) \circ ( y \bullet z ) \equiv (w \…
Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions
Murray Bremner, Sara Madariaga, Luiz A. Peresi
In part 1, we review the structure theory of , the group algebra of the symmetric group over a field of characteristic 0. We define the images o…
Permutation of elements in double semigroups
Murray Bremner, Sara Madariaga
Double semigroups have two associative operations related by the interchange relation: $( a \bullet b ) \circ ( c \bullet d ) \equiv ( a \circ c ) \bullet ( b \cir…
Jordan quadruple systems
Murray Bremner, Sara Madariaga
We define Jordan quadruple systems by the polynomial identities of degrees 4 and 7 satisfied by the Jordan tetrad {a,b,c,d} = abcd + dcba as a quadrilinear operation on associative…
Symmetric matrices, orthogonal Lie algebras, and Lie-Yamaguti algebras
Pilar Benito, Murray Bremner, Sara Madariaga
On the set H_n(K) of symmetric n by n matrices over the field K we can define various binary and ternary products which endow it with the structure of a Jordan algebra or a Lie or…
Splitting of operations for alternative and Malcev structures
Sara Madariaga
In this paper we define pre-Malcev algebras and alternative quadri-algebras and prove that they generalize pre-Lie algebras and quadri-algebras respectively to the alternative sett…
Dendriform analogues of Lie and Jordan triple systems
Murray R. Bremner, Sara Madariaga
We use computer algebra to determine all the multilinear polynomial identities of degree satisfied by the trilinear operations and $a \cdot (b \cdot c…
Gröbner-Shirshov bases for the non-symmetric operads of dendriform algebras and quadri-algebras (unabridged version)
Sara Madariaga
In this paper we use the operadic framework to find Gröbner-Shirshov bases for the free quadri-algebra. We perform computations using the representation of the nonsymmetric operad…
Special identities for the pre-Jordan product in the free dendriform algebra
Murray R. Bremner, Sara Madariaga
Pre-Jordan algebras were introduced recently in analogy with pre-Lie algebras. A pre-Jordan algebra is a vector space with a bilinear multiplication such that the p…
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…
Hopf algebras with triality
Georgia Benkart, Sara Madariaga, José M. Pérez-Izquierdo
In this paper we revisit and extend the constructions of Glauberman and Doro on groups with triality and Moufang loops to Hopf algebras. We prove that the universal enveloping alge…