19 citations · 74 across the 13 of their papers we have counts for
4 papers · 1 filter
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…