Steven R. Lippold

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20212024

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math.RA2024

Permutation-Like Matrices

Steven Robert Lippold

Permutation Matrices are a well known class of matrices which encode the elements of the symmetric group on $d$ elements as a square $d \times d$ matrix. Motivated by [4], we define…

math.RA2023

The Algebra of $S^{2}$ -Upper Triangular Matrices

Steven R. Lippold

Based on work presented in [4], we define $S^{2}$ -Upper Triangular Matrices and $S^{2}$ -Lower Triangular Matrices, two special types of $d \times d (2 d - 1)$ matrices generalizing Upper an…

math.RA2022

Existence of the Map $d e t^{S^{3}}$

Steven R. Lippold, Mihai D. Staic

In this paper we show the existence of a nontrivial linear map $d e t^{S^{3}} : V_{d}^{\otimes (3 3 d)} \to k$ with the property that $det^{S^3}(\otimes_{1\leq i<j<k\leq 3d}(v_{i,j,k})…

Permutation-Like Matrices

The Algebra of S2-Upper Triangular Matrices

Existence of the Map detS3

The Algebra of $S^{2}$ -Upper Triangular Matrices

Existence of the Map $d e t^{S^{3}}$