Lie structure on the Hochschild cohomology of a family of subalgebras of the Weyl algebra

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Samuel A Lopes (Author) FCUP; Solotar, A (Author) Other

Journal

Title: Journal of Noncommutative Geometry

Vol. 15

Pages: 1373-1407

ISSN: 1661-6952

Publisher: European Mathematical Society Publishing House

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 2 Citations

Other information

Authenticus ID: P-00V-YCJ

DOI: 10.4171/jncg/439

Abstract (EN): For each nonzero h 2 F [x], where F is a field, let Ah be the unital associative algebra generated by elements x, y, satisfying the relation yx - xy = h. This gives a parametric family of subalgebras of the Weyl algebra A1, containing many well-known algebras which have previously been studied independently. In this paper, we give a full description of the Hochschild cohomology HH'(Ah) over a field of an arbitrary characteristic. In case F has a positive characteristic, the center Z(Ah) of Ah is nontrivial and we describe HH'(Ah) as a module over Z(Ah). The most interesting results occur when F has a characteristic 0. In this case, we describe HH'(Ah) as a module over the Lie algebra HH1(Ah) and find that this action is closely related to the intermediate series modules over the Virasoro algebra. We also determine when HH'(Ah) is a semisimple HH1(Ah)-module.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 35