Power-central polynomials on matrices

Alexey Kanel-Belov, Sergey Malev, Louis Rowen

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Any multilinear non-central polynomial p (in several noncommuting variables) takes on values of degree n in the matrix algebra Mn(F) over an infinite field F. The polynomial p is called ν-central for Mn(F) if pν takes on only scalar values, with ν minimal such. Multilinear ν-central polynomials do not exist for any ν, with n>3, answering a question of Drensky and Spenko.Saltman proved a result implying that a non-central polynomial p cannot be ν-central for Mn(F), for n odd, unless ν is a product of distinct odd primes and n=mν with m prime to ν we extend this by showing for n even, that ν cannot be divisible by 4.

Original languageEnglish
Pages (from-to)2164-2176
Number of pages13
JournalJournal of Pure and Applied Algebra
Issue number6
StatePublished - 1 Jun 2016
Externally publishedYes


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