1. Quadratic nonsymmetric quaternary operads
- Author
-
Murray R. Bremner and Juana Sánchez-Ortega
- Subjects
Pure mathematics ,Algebra and Number Theory ,Rank (linear algebra) ,010102 general mathematics ,Mathematics - Rings and Algebras ,Primary 15A54, Secondary 05C05, 13P10, 13P15, 15A21, 18D50 ,Term (logic) ,Mathematics - Commutative Algebra ,Commutative Algebra (math.AC) ,16. Peace & justice ,01 natural sciences ,Permutation ,Quadratic equation ,Rings and Algebras (math.RA) ,0103 physical sciences ,Linear algebra ,FOS: Mathematics ,010307 mathematical physics ,0101 mathematics ,Algebraic number ,Commutative algebra ,Associative property ,Mathematics - Abstract
We use computational linear algebra and commutative algebra to study spaces of relations satisfied by quadrilinear operations. The relations are analogues of associativity in the sense that they are quadratic (every term involves two operations) and nonsymmetric (every term involves the identity permutation of the arguments). We focus on determining those quadratic relations whose cubic consequences have minimal or maximal rank. We approach these problems from the point of view of the theory of algebraic operads., Comment: 25 pages, 15 tables
- Published
- 2016