The images of multilinear non-associative polynomials evaluated on a\n rock-paper-scissors algebra with unit over an arbitrary field

2020/06/08 by Sergey Malev, Malev, Sergey, Coby Pines +1
Mathematics · #Advanced Topics in Algebra #Rings, Modules, and Algebras #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2006.04517

Abstract

Let mathbb F be an arbitrary field. We consider a commutative,\nnon-associative, 4-dimensional algebra mathfrak M of the rock, the paper\nand the scissors with unit over mathbb F and we prove that the image over\n mathfrak M of every non-associative multilinear polynomial over mathbb\nF is a vector space. The same question we consider for two subalgebras: an\nalgebra of the rock, the paper and the scissors without unit, and an algebra of\ntrace zero elements with zero scalar part. Moreover in this paper we consider\nthe questions of possible evaluations of homogeneous polynomials on these\nalgebras.\n

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