Differential Operators on the free algebras
Uma N.Iyer, Timothy C.McCune
TL;DR
This paper characterizes and studies properties of differential operators, including $eta$- and quantum differential operators, on free associative algebras, expanding understanding of noncommutative algebraic structures.
Contribution
It provides a detailed description and analysis of differential operators on free associative algebras, extending previous definitions to this specific algebra class.
Findings
Explicit descriptions of differential operators on free algebras
Analysis of properties of these operators in noncommutative context
Extension of existing operator frameworks to free associative algebras
Abstract
Following the definitions of the algebras of differential operators, -differential operators, and the quantum differential operators on a noncommutative (graded) algebra given in \cite{LR}, we describe these operators on the free associative algebra. We further study their properties.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons