Maps from the enveloping algebra of the positive Witt algebra to regular algebras

Susan J. Sierra and Chelsea Walton

Vol. 284 (2016), No. 2, 475–509

DOI: 10.2140/pjm.2016.284.475

Abstract

We construct homomorphisms from the universal enveloping algebra of the positive (part of the) Witt algebra to several different Artin–Schelter regular algebras, and determine their kernels and images. As a result, we produce elementary proofs that the universal enveloping algebras of the Virasoro algebra, the Witt algebra, and the positive Witt algebra are neither left nor right noetherian.

Keywords

Artin–Schelter regular, Jordan plane, non-noetherian, universal enveloping algebra, Witt algebra

Mathematical Subject Classification 2010

Primary: 14A22, 16S30, 16S38, 17B68

Milestones

Received: 2 September 2015

Revised: 4 May 2016

Accepted: 4 May 2016

Published: 30 August 2016