
TL;DR
This paper classifies three-dimensional quantum zero curvature representations and tetrahedron equations, deriving R-matrices that connect Bose and Fermi oscillators, and relates them to super-algebras through compactification.
Contribution
It introduces a comprehensive classification scheme for 3D quantum zero curvature representations, including super-algebras and super-tetrahedron equations, with explicit R-matrices.
Findings
Derived R-matrices intertwining Bose and Fermi oscillators
Reproduced super-algebras U_q(gl(n|m)) via 3d->2d compactification
Classified algebraic structures with parity components
Abstract
In this paper we give a detailed classification scheme for three-dimensional quantum zero curvature representation and tetrahedron equations. This scheme includes both even and odd parity components, the resulting algebras of observables are either Bose q-oscillators or Fermi oscillators. Three-dimensional -matrices intertwining variously oriented tensor products of Bose and Fermi oscillators and satisfying tetrahedron and super-tetrahedron equations are derived. The 3d->2d compactification reproduces U_q(gl(n|m)) super-algebras and their representation theory.
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.
