Maximal and primitive elements in Weyl modules for type \(A_2\)
type: Item
instance of: scholarly article
title: Maximal and primitive elements in Weyl modules for type \(A_2\)
zbMATH Open document ID: 0932.17017
author: Nanhua Xi
published in: Journal of Algebra
publication date: 2000-03-12T00:00:00Z
review text: The author finds all maximal and primitive elements in Verma modules of the quantized Frobenius kernel and Weyl modules for type \(A_2\). The quantized enveloping algebras are at roots of unity. His methods are based on the results of his earlier paper [Publ. Res. Inst. Math. Sci. 32, 235-276 (1996; Zbl 0874.17013)] and on some ideas of \textit{R. S. Irving} [J. Algebra 99, 438-457 (1986; Zbl 0598.20052)], who determined the submodule structure of Weyl modules for \(SL_3\). The author promises similar results for type \(B_2\) in the near future.
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 1309135
zbMATH Keywords: maximal elements
zbMATH Keywords: primitive elements
zbMATH Keywords: Verma modules
zbMATH Keywords: quantized Frobenius kernel
zbMATH Keywords: Weyl modules
reviewed by: Earl J. Taft
MaRDI profile type: Publication
full work available at URL: jabr.1998.7766
OpenAlex ID: W2029877391
cites work: The submodule structure of Weyl modules for \(SL_ 3\)
cites work: The structure of certain highest weight modules for \(SL_ 3\)
cites work: Q3699004
cites work: Q3816243
cites work: Finite Dimensional Hopf Algebras Arising From Quantized Universal Enveloping Algebras
cites work: Quantum groups at roots of 1
cites work: Introduction to quantum groups
cites work: Irreducible modules of quantized enveloping algebras at roots of 1
DOI: 10.1006/JABR.1998.7766
description: scientific article; zbMATH DE number 1309135