Related papers: Polynomial Detection of Matrix Subalgebras

This paper establishes new upper bounds for the right eigenvalues of monic matrix polynomials over the quaternion division algebra. The noncommutative nature of quaternion multiplication presents fundamental challenges in eigenvalue…

We count matrices in the special linear group SL(n, Z) whose characteristic polynomials split completely over Q.

The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between…

A notion of Drinfeld polynomials is introduced for modules of two-parameter quantum affine algebras. Finite dimensional representations are then characterized by sets of $l$-tuples of pairs of Drinfeld polynomials with certain conditions.

We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most r. We apply these methods to several cases including the case r = 6 in the space of bilinear maps C^4 x C^4 -> C^4. This…

We introduce a new approach to the classification of operator identities, based on basic concepts from the theory of algebraic operads together with computational commutative algebra applied to determinantal ideals of matrices over…

We examine the capacity of the complementarity spectrum to distinguish non-isomorphic digraphs. We focus on the seven families with exactly three complementarity eigenvalues. Our findings reveal that in some, but not all families, any two…

We show that the bilinear complexity of multiplication in a non-split quaternion algebra over a field of characteristic distinct from 2 is 8. This question is motivated by the problem of characterising algebras of almost minimal rank…

An algorithm for factoring polynomials over finite fields is given by Berlekamp in 1967. The main tool was the matrix Q corresponding to each polynomial. This paper studies the degrees of polynomials over binary field that associated with…

We prove that two finite prime $\Omega$-algebras defined over the same unital commutative ring and satisfying the same set of polynomial identities are isomorphic.

Let $k$ be a field of characteristic two. We prove that a non constant monic polynomial $f\in k[X]$ of degree $n$ is the minimal/characteristic polynomial of a symmetric matrix with entries in $k$ if and only if it is not the product of…

We study polynomial functors in the incompressible category $\text{Ver}_4^+$, which can be viewed as super polynomial functors in characteristic 2. Concretely, we classify additive, exact and simple polynomial functors, and describe how…

We introduce two remarkable identities written in terms of single commutators and anticommutators for any three elements of arbitrary associative algebra. One is a consequence of other (fundamental identity). From the fundamental identity,…

Let $p$ be a multilinear polynomial in several non-commuting variables with coefficients in an arbitrary field $K$. Kaplansky conjectured that for any $n$, the image of $p$ evaluated on the set $M_n(K)$ of $n$ by $n$ matrices is either…

We prove that a maximal totally complex submanifold $N^{2n}$ of the quaternionic projective space $\mathbb{H}\mathbb{P}^n$ ($n\geq 2$) is a parallel submanifold, provided one of the following conditions is satisfied: (1) $N$ is the orbit of…

In the present paper we review our project of systematic construction of invariant differential operators on the example of the non-compact algebras su(n,n) for n=2,3,4. We give explicitly the main multiplets of indecomposable elementary…

We investigate the problem asking when any square matrix whose entries lie in a finite field of characteristic 2 is decomposable into the sum of a diagonalizable matrix and a nilpotent matrix with index of nilpotency at most 2 and, as a…

We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.

We classify the subalgebras of the general Lie conformal algebra $\gc_N$ that act irreducibly on $\C[\partial]^N$ and that are normalized by the $\operatorname{sl}_2$--part of a Virasoro element. The problem turns out to be closely related…

In this paper we prove that a matrix property of nettedness (all 2x2 cells satisfy a recurrence) is preserved for powers of such a matrix, where the coefficients are all instances of the same sequence. Also, we find an n-dimensional analog…