Details:
Title  Jordan quadruple systems  Author(s)  Murray R. Bremner, Sara Madariaga  Type  Article in Journal  Abstract  Abstract We define Jordan quadruple systems by the polynomial identities of degrees 4 and 7 satisfied by the Jordan tetrad a , b , c , d = a b c d + d c b a as a quadrilinear operation on associative algebras. We find further identities in degree 10 which are not consequences of the defining identities. We introduce four infinite families of finite dimensional Jordan quadruple systems, and construct the universal associative envelope for a small system in each family. We obtain analogous results for the antitetrad [ a , b , c , d ] = a b c d − d c b a . Our methods rely on computer algebra, especially linear algebra on large matrices, the LLL algorithm for lattice basis reduction, representation theory of the symmetric group, noncommutative Gröbner bases, and Wedderburn decompositions of associative algebras.  Keywords  Jordan tetrad, Polynomial identities, Gröbner bases, Universal associative envelopes, Wedderburn decompositions  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869314002403 
Language  English  Journal  Journal of Algebra  Volume  412  Pages  51  86  Year  2014  Edition  0  Translation 
No  Refereed 
No 
