On restricted simple modules of contact Lie superalgebras of odd type
Sign Up to like & getrecommendations! 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
Sign Up to like & getrecommendations! 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
Sign Up to like & getrecommendations! 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
Sign Up to like & getrecommendations! 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
Sign Up to like & getrecommendations! 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)
Sign Up to like & getrecommendations! 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
Simple modules over the Takiff Lie algebra for sl2
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Mathematical Physics"
DOI: 10.1063/5.0157958
Abstract: In this paper, we construct, investigate and, in some cases, classify several new classes of (simple) modules over the Takiff sl2. More precisely, we first explicitly construct and classify, up to isomorphism, all modules over… read more here.
Keywords: takiff lie; simple modules; algebra; modules takiff ... See more keywords
Three-vertex prime graphs and reality of trees
Sign Up to like & getrecommendations! 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
Laurent family of simple modules over quiver Hecke algebras
Sign Up to like & getrecommendations! Published in 2024 at "Compositio Mathematica"
DOI: 10.1112/s0010437x24007310
Abstract: We introduce the notions of quasi-Laurent and Laurent families of simple modules over quiver Hecke algebras of arbitrary symmetrizable types. We prove that such a family plays a similar role of a cluster in quantum… read more here.
Keywords: quiver hecke; family; simple modules; algebra ... See more keywords