On SAGBI bases theory of skew Poincar\'e-Birkhoff-Witt extensions
Y\'esica Su\'arez, Armando Reyes
TL;DR
This paper initiates the development of SAGBI bases theory for skew Poincaré-Birkhoff-Witt extensions and explores polynomial composition within their subalgebras.
Contribution
It introduces the first approach to SAGBI bases theory in the context of skew Poincaré-Birkhoff-Witt extensions and examines polynomial composition problems.
Findings
Preliminary SAGBI bases framework established for skew PBW extensions
Analysis of polynomial composition problems in subalgebras of these extensions
Foundations laid for further algebraic and computational studies
Abstract
In this paper we present a first approach toward a \texttt{SAGBI} bases theory of skew Poincar\'e-Birkhoff-Witt extensions, and investigate the problem of polynomial composition for \texttt{SAGBI} bases of subalgebras of these extensions.
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