AN ASSOCIATIVE TRIPLE SYSTEM OF THE SECOND KIND

作者：Beites P D; Nicolas A P^*

来源：Communications in Algebra, 2016, 44(11): 5027-5043.

DOI：10.1080/009278722016.1149185

• Automorphism
• Composition algebra
• Computational linear algebra
• Filippov algebra
• Identities

We study the associative triple system of the second kind A obtained from a new multiplication defined in the underlying vector space of the four-dimensional ternary Filippov algebra A(4). Descriptions of the automorphisms group and the antiautomorphisms set of A, both constituted by certain orthogonal matrices, are presented. Through a Leibniz-type formula for a power of a derivation of A, the link between the mentioned group and the Lie algebra of derivations of A is established. Applying the random vectors method, which involves computational linear algebra on matrices, level 3 identities of A are determined. Moreover, levels 1 and 2 identities of certain reduced algebras that are composition algebras, some Hurwitz too and others isomorphic to standard composition algebras, are also calculated.

• 出版日期2016