LAUSR

On restricted simple modules of contact Lie superalgebras of odd type

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1 Published in 2017 at "Mathematische Nachrichten"

DOI: 10.1002/mana.201600478

Abstract: For contact Lie superalgebras of odd type over an algebraically closed field of characteristic p>3, the composition factors of Kac modules and the character formulas for all the restricted simple modules are explicitly determined. And… read more here.

Keywords: lie superalgebras; odd type; restricted simple; superalgebras odd ... See more keywords

Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras

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0 Published in 2018 at "Mathematische Zeitschrift"

DOI: 10.1007/s00209-020-02510-y

Abstract: We prove that the tensor product of a simple and a finite dimensional $${\mathfrak {sl}}_n$$ sl n -module has finite type socle. This is applied to reduce classification of simple $${\mathfrak {q}}(n)$$ q ( n… read more here.

Keywords: algebras simple; lie algebras; simple mathfrak; translated simple ... See more keywords

Higher Jones Algebras and their Simple Modules

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1 Published in 2019 at "Algebras and Representation Theory"

DOI: 10.1007/s10468-018-09853-5

Abstract: Let G be a connected reductive algebraic group over a field of positive characteristic p and denote by T $\mathcal T$ the category of tilting modules for G . The higher Jones algebras are the… read more here.

Keywords: modules higher; algebras simple; higher jones; jones algebras ... See more keywords

On the number of simple modules in a block of a finite group

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1 Published in 2017 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2016.10.022

Abstract: Abstract We prove that if B is a p-block with non-trivial defect group D of a finite p-solvable group G, then l ( B ) p r , where r is the sectional rank of… read more here.

Keywords: number simple; modules block; group; finite group ... See more keywords

The first cohomology of sl(2,1) with coefficients in χ-reduced Kac modules and simple modules

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1 Published in 2020 at "Journal of Pure and Applied Algebra"

DOI: 10.1016/j.jpaa.2020.106403

Abstract: Abstract Over a field of characteristic p > 2 , the first cohomology of the special linear Lie superalgebra sl ( 2 , 1 ) with coefficients in all χ-reduced Kac modules and simple modules… read more here.

Keywords: first cohomology; kac modules; coefficients reduced; modules simple ... See more keywords

THE PRIME IDEALS AND SIMPLE MODULES OF THE UNIVERSAL ENVELOPING ALGEBRA U(𝔟⋉V2)

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0 Published in 2019 at "Glasgow Mathematical Journal"

DOI: 10.1017/s0017089519000302

Abstract: Abstract Let 𝔟 be the Borel subalgebra of the Lie algebra 𝔰𝔩2 and V2 be the simple two-dimensional 𝔰𝔩2-module. For the universal enveloping algebra $\[{\cal A}: = U(\gb \ltimes {V_2})\]$ of the semi-direct product 𝔟⋉V2… read more here.

Keywords: prime ideals; universal enveloping; simple modules; modules universal ... See more keywords

Three-vertex prime graphs and reality of trees

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2 Published in 2022 at "Communications in Algebra"

DOI: 10.1080/00927872.2023.2196345

Abstract: We continue the study of prime simple modules for quantum affine algebras from the perspective of $q$-fatorization graphs. In this paper we establish several properties related to simple modules whose $q$-factorization graphs are afforded by… read more here.

Keywords: simple modules; graphs reality; prime graphs; vertex prime ... See more keywords