Vol. 311, No. 2, 2021

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Frobenius nil-Hecke algebras

Alistair Savage and John Stuart

Vol. 311 (2021), No. 2, 455–473
Abstract

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

Keywords
nilCoxeter algebra, nilHecke algebra, Frobenius algebra, divided difference operator, Demazure operator
Mathematical Subject Classification
Primary: 20C08
Milestones
Received: 25 August 2020
Accepted: 27 January 2021
Published: 31 July 2021
Authors
Alistair Savage
Department of Mathematics and Statistics
University of Ottawa
Ottawa, ON
Canada
John Stuart
Department of Mathematics and Statistics
University of Ottawa
Ottawa, ON
Canada