Frobenius nilHecke algebras

TL;DR

This paper introduces a new class of Frobenius nilHecke algebras associated with Frobenius superalgebras, generalizing classical and odd nilHecke algebras through Frobenius divided difference operators.

Contribution

It constructs Frobenius nilHecke algebras for any Frobenius superalgebra and explores their relations to classical and odd nilHecke algebras, including Morita equivalences.

Findings

Recover classical nilHecke algebras when A is the ground ring.

Establish Morita equivalence with odd nilHecke algebras when A is the Clifford algebra.

Define Frobenius divided difference operators acting on Frobenius polynomial algebras.

Abstract

To any Frobenius superalgebra $A$ we associate towers of Frobenius nilCoxeter algebras and Frobenius nilHecke algebras. These act naturally, via Frobenius divided difference operators, on Frobenius polynomial algebras. When $A$ is the ground ring, our algebras recover the classical nilCoxeter and nilHecke algebras. When $A$ is the two-dimensional Clifford algebra, they are Morita equivalent to the odd nilCoxeter and odd nilHecke algebras.