2007/01/22 by Francesca Benanti, Vesselin Drensky, Benanti, Francesca +1
Mathematics · #13A50 #15A72 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Primary: 16R30 #Rings and Algebras (math.RA) #Secondary: 16S15 #math.RA #msc:13A50 #msc:15A72 #msc:16R30 #msc:16S15
paper · pdf · doi:10.48550/arxiv.math/0701609
arxiv created 2007/01/22 · openalex publication_date 2007/01/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The trace algebra C(n,d) over a field of characteristic 0 is generated by all traces of products of d generic nxn matrices, n,d>1. Minimal sets of generators of C(n,d) are known for n=2 and n=3 for any d as well as for n=4 and n=5 and d=2. The defining relations between the generators are found for n=2 and any d and for n=3, d=2 only. Starting with the generating set of C(3,d) given by Abeasis and Pittaluga in 1989, we have shown that the minimal degree of the set of defining relations of C(3,d) is equal to 7 for any d>2. We have determined all relations of minimal degree. For d=3 we have also found the defining relations of degree 8. The proofs are based on methods of representation theory of the general linear group and easy computer calculations with standard functions of Maple.