On the nilpotency degree of the algebra with identity xⁿ=0

2011/06/06 by Artem Lopatin, Lopatin, Artem A.
Engineering · Mathematics · #16N40 #16R10 #16R30 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1106.0950

openalex publication_date 2011/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Denote by C_n,d the nilpotency degree of a relatively free algebra generated by d elements and satisfying the identity xⁿ=0. Under assumption that the characteristic p of the base field is greater than n/2, it is shown that C_n,d n/2. For p≠2 the nilpotency degree C_4,d is described with deviation 4 for all d. As an application, a finite generating set for the algebra R^GL(n) of GL(n)-invariants of d matrices is established in terms of C_n,d. Several conjectures are formulated.

Citations

• The invariant theory of n × n matrices

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