Ilan Levin

activity

20232026

most citedAlternating Roots of Polynomials over Cayley-Dickson Algebras

2 citations · 3 across the 8 of their papers we have counts for

collaborators

8 papers

math.RA2026

General Polynomials and Eigenvalues Over Cayley--Dickson Algebras

Adam Chapman, Ilan Levin, Solomon Vishkautsan

In this paper, we provide an explicit method for determining the zero set of monic quadratic general polynomials over Cayley--Dickson algebras with any base field of characteristic…

math.RA2026

Central Products of Cayley-Dickson Loops

Adam Chapman, Ilan Levin

This paper studies the triviality of commutators in central products of Cayley-Dickson loops. Two immediate outcomes of this study are (1) the construction of a sequence of non-com…

math.RA2025

Cyclic Division Algebras of Odd Prime Degree are never Amitsur-Small

Adam Chapman, Ilan Levin, Marco Zaninelli

A division ring $D$ is Amitsur-Small if for every $n$ and every maximal left ideal $I$ in $D [x_{1}, \dots, x_{n}]$ , $I \cap D [x_{1}, \dots, x_{n - 1}]$ is maximal in $D [x_{1}, \dots, x_{n - 1}]$ . Th…

math.GR2025

How Associative Can a Non-Associative Moufang Loop Be?

Ilan Levin

We prove a non-associative analog to the well-known $\frac{5}{8}$ Theorem. Namely, for a finite Moufang loop with nuclear commutators, we show that if the probability that three ra…

math.CO2024★ 1 cited

Loops with involution and the Cayley-Dickson doubling process

Adam Chapman, Ilan Levin, Uzi Vishne +1

We develop a theory of loops with involution. On this basis we define a Cayley-Dickson doubling on loops, and use it to investigate the lattice of varieties of loops with involutio…

math.KT2024

Invariant for Sets of Pfister Forms

Adam Chapman, Ilan Levin

We associate an $(n_{1} + \dots + n_{t} - k (t - 1))$ -fold Pfister form to any $t$ -tuple of $k$ -linked Pfister forms of dimensions $2^{n_{1}}, \dots, 2^{n_{t}}$ , and prove its invariance under the di…

math.RA2023★ 2 cited

Alternating Roots of Polynomials over Cayley-Dickson Algebras

Adam Chapman, Ilan Levin

We introduce the notions of alternating roots of polynomials and alternating polynomials over a Cayley-Dickson algebra, and prove a connection between the alternating roots of a gi…

math.RA2023

Chain Lemma, Quadratic Forms and Symbol Length

Adam Chapman, Ilan Levin

We want to bound the symbol length of classes in $_{2^{m - 1}} B r (F)$ which are represented by tensor products of 5 or 6 cyclic algebras of degree $2^{m}$ . The main ingredients are th…