On rational twisted generalized Weyl algebra
Natalia Golovashchuk, Jo\~ao Schwarz

TL;DR
This paper explores the structure of rational twisted generalized Weyl algebras, providing explicit formulas and constructions based on Lie algebra representations, with applications to special unitary and orthogonal algebras of rank three.
Contribution
It introduces a new construction method for rational twisted generalized Weyl algebras using Gelfand-Zeitlin realization, expanding understanding of their structure and involution-invariant subalgebras.
Findings
Explicit formulas for algebra constructions
Description of involution-symmetric subalgebras
Applications to rank three unitary and orthogonal algebras
Abstract
The aim of this work is to investigate the structure of some skew twisted algebras, when the coefficient ring is a localization of the polynomial ring over the field of characteristic zero, and an involution is provided. A parallel construction of the rational twisted generalized Weyl algebras is given. We propose a method and explicit formulas for a constructive description of these algebras and their involution-symmetric invariant subalgebras based on the Gelfand-Zeitlin realization of the universal enveloping algebra of some complex Lie algebras. As concrete examples we discuss special unitary and orthogonal algebras of rank three.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons
