A. Berele

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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…