Conjugation in Representations of the Zassenhaus Algebra

Bin Shu

doi:10.1007/s101140000066

Conjugation in Representations of the Zassenhaus Algebra

Bin Shu

Shanghai Maritime University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let F be an algebracially closed field of characteristic p > 2, and L be the pⁿ-dimensional Zassenhaus algebra with the maximal invariant subalgebra L₀ and the standard filtration {L_i}|^pn-2_i=-1. Then the number of isomorphism classes of simple L-modules is equal to that of simple L₀-modules, corresponding to an arbitrary character of L except when its height is biggest. As to the number corresponding to the exception there was an earlier result saying that it is not bigger than pⁿ.

Original language	English
Pages (from-to)	319-326
Number of pages	8
Journal	Acta Mathematica Sinica, English Series
Volume	17
Issue number	2
DOIs	https://doi.org/10.1007/s101140000066
State	Published - 2001
Externally published	Yes

Keywords

Simple modules of lie algebras and their isomorphism classes
Zassenhaus algebras (Cartan-type Lie algebras)

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10.1007/s101140000066

Cite this

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abstract = "Let F be an algebracially closed field of characteristic p > 2, and L be the pn-dimensional Zassenhaus algebra with the maximal invariant subalgebra L0 and the standard filtration \{Li\}|pn-2i=-1. Then the number of isomorphism classes of simple L-modules is equal to that of simple L0-modules, corresponding to an arbitrary character of L except when its height is biggest. As to the number corresponding to the exception there was an earlier result saying that it is not bigger than pn.",

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AB - Let F be an algebracially closed field of characteristic p > 2, and L be the pn-dimensional Zassenhaus algebra with the maximal invariant subalgebra L0 and the standard filtration {Li}|pn-2i=-1. Then the number of isomorphism classes of simple L-modules is equal to that of simple L0-modules, corresponding to an arbitrary character of L except when its height is biggest. As to the number corresponding to the exception there was an earlier result saying that it is not bigger than pn.

KW - Simple modules of lie algebras and their isomorphism classes

KW - Zassenhaus algebras (Cartan-type Lie algebras)

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ER -

Conjugation in Representations of the Zassenhaus Algebra

Abstract

Keywords

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