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Abstract
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To any Frobenius superalgebra
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
is
the ground ring, our algebras recover the classical nil-Coxeter and nil-Hecke algebras.
When
is
the two-dimensional Clifford algebra, they are Morita equivalent to the odd
nil-Coxeter and odd nil-Hecke algebras.
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Keywords
nilCoxeter algebra, nilHecke algebra, Frobenius algebra,
divided difference operator, Demazure operator
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Mathematical Subject Classification
Primary: 20C08
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Milestones
Received: 25 August 2020
Accepted: 27 January 2021
Published: 31 July 2021
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