Finite-Dimensional Representations of Hyper Multicurrent and Multiloop Algebras

Autor: Angelo Bianchi, Samuel Chamberlin
Rok vydání: 2020
Předmět:
Zdroj: Algebras and Representation Theory. 24:453-472
ISSN: 1572-9079
1386-923X
DOI: 10.1007/s10468-020-09955-z
Popis: We investigate the categories of finite-dimensional representations of multicurrent and multiloop hyperalgebras in positive characteristic, i.e., the hyperalgebras associated to the multicurrent algebras $\mathfrak g\otimes\mathbb{C}[t_1,\ldots,t_n]$ and to the multiloop algebras $\mathfrak g\otimes\mathbb{C}[t_1^{\pm1},\ldots,t_n^{\pm 1}]$, where $\mathfrak g$ is any finite-dimensional complex simple Lie algebra. The main results are the construction of the universal finite-dimensional highest-weight modules and a classification of irreducible modules in each category. In the characteristic zero setting we also provide a relationship between them.
The paper was revised for publication, some details were added and few typos were fixed
Databáze: OpenAIRE
Externí odkaz: