Quantum generalized Heisenberg algebras and their representations

• Tipo: Artigo em Revista Científica Internacional
• Data: 2022

Autores

Samuel A Lopes (Autor) FCUP; Razavinia, F (Autor) Outra

Revista

Título: Communications in Algebra

Vol. 50

Páginas: 463-483

ISSN: 0092-7872

Editora: Taylor & Francis

Indexação

ISI Web of Knowledge - 1 Citação

Scopus - 4 Citações

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 21