(k+1)-potent Matrices in triangular matrix Groups and Incidence Algebras of Finite Posets

2020/08/30 by Ivan Gargate, Gargate, Ivan, Michael Gargate +1
Engineering · Mathematics · #15B33 #16S50 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2009.04243

openalex publication_date 2020/08/30 · openalex created_date 2020/09/14 · openalex updated_date 2026/07/28

Abstract

Let \mathbbK be a field such that char(\mathbbK)\nmid k and char(\mathbbK)\nmid k+1. We describe all (k+1)-potent matrices over the group of upper triangular matrix. In the case that \mathbbK is a finite field we show how to compute the number of these elements in triangular matrix groups and use this formula to compute the number of (k+1)-potent elements in the Incidence Algebra I(X,\mathbbK) where X is a finite poset.

Citations

• When is a matrix a difference of two idempotents
• When is a matrix a sum of idempotents?

Related

• Counting Elements on Full Matrix Groups over Finite Field with Prescribed Eigenvalues
• Reduction for characters of finite algebra groups
• Sums Of K-potent Matrices
• K₀-theory of n-potents in rings and algebras
• Involutions on Incidence Algebras of Finite Posets