@article{4734d1b519364201a28ca417bf82e8fb,

title = "Maps from the enveloping algebra of the positive witt algebra to regular algebras",

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, theWitt algebra, and the positiveWitt algebra are neither left nor right noetherian.",

keywords = "Artin-Schelter regular, Jordan plane, Non-noetherian, Universal enveloping algebra, Witt algebra",

author = "Sierra, {Susan J.} and Chelsea Walton",

note = "Funding Information: C. Walton was supported by the US National Science Foundation grant #1550306. We thank MIT and the NSF for supporting a visit by the first author to MIT in February 2015, in which much of the work on this paper was done. We thank Jacques Alev, Jason Bell, and Lance Small for helpful discussions. In addition, we thank the referee for pointing us to [Conley and Martin 2007] and for prompting Remarks 3.14 and 5.15. Publisher Copyright: {\textcopyright} 2016 Mathematical Sciences Publishers.",

year = "2016",

doi = "10.2140/pjm.2016.284.475",

language = "English (US)",

volume = "284",

pages = "475--509",

journal = "Pacific Journal of Mathematics",

issn = "0030-8730",

publisher = "University of California, Berkeley",

number = "2",

}