A. Berele

collaborators

5 papers

math.RT2026

Polynomial identities for quivers via incidence algebras

Allan Berele, Giovanni Cerulli Irelli, Javier De Loera ChÃ¡vez +1

We show that the path algebra of a quiver satisfies the same polynomial identities of an algebra of matrices, if any. In particular, the algebra of nxn matrices is PI-equivalent to…

math.MG2026

The Perimeter Winternitz Theorem in a Triangle

Allan Berele, Stefan Catoiu

A variable line through the centroid G of a triangle divides the triangle into two parts each of whose lengths as a fraction of the perimeter fills a closed interval [m,1-m], with…

math.RA2025

Invariants of Superalgebras as Complex Integrals

Allan Berele

In [A. Berele, Computing super matrix invariants, {\it Advances in Applied Math. \bf48} (2012), 273--289.] we defined integrals that approximated the PoincarÃ© series of the invari…

math.RA2025

Integrality and Specialized Symmetric Functions

Allan Berele

Given $d_{1}, \dots, d_{k}$ in the field $F$ , there is a weighted trace function $F^{k} \to F$ given by $t r (x_{1}, \dots, x_{k}) = \sum d_{i} x_{i}$ . We prove that $F^{k}$ satisfies trace identi…

math.RA2025

Two-Term Polynomial Identities

Allan Berele, Peter Danchev, Bridget Eileen Tenner

We study algebras satisfying a two-term multilinear identity, namely one of the form $x_{1} \dots x_{n} = q x_{I ¨ (1)} \dots x_{I ¨ (n)}$ , where $q$ is a parameter from the base field. W…