2010/08/16 by Murray R. Bremner, Bremner, Murray R., Luiz A. Peresi +1 · 1 citation
Computer Science · Mathematics · #17A32 #17A50 #17C05 #17C40 #17C50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Primary 17A30. Secondary 17A15 #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1008.2723
openalex publication_date 2010/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Semispecial quasi-Jordan algebras (also called Jordan dialgebras) are defined by the polynomial identities a(bc) = a(cb), (ba)a2 = (ba2)a, and (b,a2,c) = 2(b,a,c)a. These identities are satisfied by the product ab = a \dashv b + b \vdash a in an associative dialgebra. We use computer algebra to show that every identity for this product in degree ≤ 7 is a consequence of the three identities in degree ≤ 4, but that six new identities exist in degree 8. Some but not all of these new identities are noncommutative preimages of the Glennie identity.