Radford bases and Sch\"utzenberger's Factorizations
Matthieu Deneufch\^atel, G\'erard H. E. Duchamp, Vincel Hoang Ngoc, Minh
TL;DR
This paper extends Schützenberger's factorization to all Lie algebras with ordered bases and explores its relation to Poincaré-Birkhoff-Witt bases and their duals, broadening its applicability.
Contribution
It generalizes Schützenberger's factorization beyond specific combinatorial contexts to all Lie algebras with ordered bases.
Findings
Schützenberger's factorization applies to all Lie algebras with ordered bases.
Relations between Poincaré-Birkhoff-Witt bases and dual families are clarified.
The extension broadens the theoretical framework of algebraic factorizations.
Abstract
In this paper, we present Sch\"utzenberger's factorization in different combinatorial contexts and show that its validity is not restricted to these cases but can be extended to every Lie algebra endowed with an ordered basis. We also expose some elements of the relations between the Poincar\'e-Birkhoff-Witt bases of the enveloping algebra and their dual families.
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Taxonomy
TopicsAdvanced Topics in Algebra · graph theory and CDMA systems · Rings, Modules, and Algebras