Quantum generalized Heisenberg algebras and their representations

• Type: Article in International Scientific Journal
• Date: 2022

Authors

Samuel A Lopes (Author) FCUP; Razavinia, F (Author) Other

Journal

Title: Communications in Algebra

Vol. 50

Pages: 463-483

ISSN: 0092-7872

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 4 Citations

Other information

Authenticus ID: P-00V-AFS

DOI: 10.1080/00927872.2021.1959602

Abstract (EN): We introduce and study a new class of algebras, which we name quantum generalized Heisenberg algebras (qGHA), including both the so-called generalized Heisenberg algebras and the generalized down-up algebras, but allowing more parameters of freedom, so as to encompass a wider range of applications and provide a common framework for several previously studied classes of algebras. In particular, our class includes the enveloping algebras of the Lie algebra sl2 and of the 3-dimensional Heisenberg Lie algebra, as well as its q-deformation, neither of which can be realized as a generalized Heisenberg algebra. This paper focuses mostly on the classification of finite-dimensional irreducible representations of qGHA, a study which reveals their rich structure. Although these algebras are not in general noetherian, their representations still retain a Lie-theoretic flavor. We work over a field of arbitrary characteristic and our results are presented in a characteristic-free fashion.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 21