Simple modules for some Cartan-type Lie superalgebras

2015 ◽  
Vol 1 (1032) ◽  
Author(s):  
Zhu Wei ◽  
Yongzheng Zhang
Keyword(s):  
Lie Superalgebras ◽  
Simple Modules ◽  
Cartan Type

scholarly journals Primitive ideals, twisting functors and star actions for classical Lie superalgebras

2016 ◽  
Vol 2016 (718) ◽  
Author(s):  
Kevin Coulembier ◽  
Volodymyr Mazorchuk
Keyword(s):  
Representation Theory ◽  
Lie Superalgebras ◽  
Simple Modules ◽  
Primitive Ideals

AbstractWe study three related topics in representation theory of classical Lie superalgebras. The first one is classification of primitive ideals, i.e. annihilator ideals of simple modules, and inclusions between them. The second topic concerns Arkhipov’s twisting functors on the BGG category

The Finite-dimensional Modular Lie Superalgebra Γ

2010 ◽  
Vol 17 (03) ◽  
pp. 525-540 ◽  
Author(s):  
Xiaoning Xu ◽  
Yongzheng Zhang ◽  
Liangyun Chen
Keyword(s):  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Explicit Description ◽  
Cartan Type ◽  
Modular Lie Superalgebra ◽  
New Family ◽  
Finite Dimensional ◽  
Derivation Superalgebra ◽  
Modular Lie Superalgebras

A new family of finite-dimensional modular Lie superalgebras Γ is defined. The simplicity and generators of Γ are studied and an explicit description of the derivation superalgebra of Γ is given. Moreover, it is proved that Γ is not isomorphic to any known Lie superalgebra of Cartan type.

scholarly journals Complexity for modules over the classical Lie superalgebra

2012 ◽  
Vol 148 (5) ◽  
pp. 1561-1592 ◽  
Author(s):  
Brian D. Boe ◽  
Jonathan R. Kujawa ◽  
Daniel K. Nakano
Keyword(s):  
Lie Algebra ◽  
Lie Superalgebra ◽  
Projective Resolution ◽  
Lie Superalgebras ◽  
Simple Modules ◽  
Minimal Projective Resolution ◽  
Finite Dimensional ◽  
Reductive Lie Algebra ◽  
Completely Reducible ◽  
Kac Modules

AbstractLet ${\Xmathfrak g}={\Xmathfrak g}_{\zerox }\oplus {\Xmathfrak g}_{\onex }$ be a classical Lie superalgebra and let ℱ be the category of finite-dimensional ${\Xmathfrak g}$-supermodules which are completely reducible over the reductive Lie algebra ${\Xmathfrak g}_{\zerox }$. In [B. D. Boe, J. R. Kujawa and D. K. Nakano, Complexity and module varieties for classical Lie superalgebras, Int. Math. Res. Not. IMRN (2011), 696–724], we demonstrated that for any module M in ℱ the rate of growth of the minimal projective resolution (i.e. the complexity of M) is bounded by the dimension of ${\Xmathfrak g}_{\onex }$. In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra $\Xmathfrak {gl}(m|n)$. In both cases we show that the complexity is related to the atypicality of the block containing the module.

Restricted Envelopes of Lie Superalgebras

2015 ◽  
Vol 22 (02) ◽  
pp. 309-320
Author(s):  
Liping Sun ◽  
Wende Liu ◽  
Xiaocheng Gao ◽  
Boying Wu
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Cartan Type ◽  
Modular Lie Algebras ◽  
Modular Lie Superalgebras

Certain important results concerning p-envelopes of modular Lie algebras are generalized to the super-case. In particular, any p-envelope of the Lie algebra of a Lie superalgebra can be naturally extended to a restricted envelope of the Lie superalgebra. As an application, a theorem on the representations of Lie superalgebras is given, which is a super-version of Iwasawa's theorem in Lie algebra case. As an example, the minimal restricted envelopes are computed for three series of modular Lie superalgebras of Cartan type.

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

2020 ◽  
Author(s):  
Chih-Whi Chen ◽  
Kevin Coulembier ◽  
Volodymyr Mazorchuk
Keyword(s):  
Lie Algebras ◽  
Lie Superalgebras ◽  
Simple Modules

On restricted simple modules of contact Lie superalgebras of odd type

2017 ◽  
Vol 290 (17-18) ◽  
pp. 2934-2947
Author(s):  
Wende Liu ◽  
Shujuan Wang ◽  
Jixia Yuan
Keyword(s):  
Lie Superalgebras ◽  
Simple Modules

scholarly journals MAXIMAL SUBALGEBRAS FOR MODULAR GRADED LIE SUPERALGEBRAS OF ODD CARTAN TYPE

2015 ◽  
Vol 20 (4) ◽  
pp. 1075-1106 ◽  
Author(s):  
WENDE LIU ◽  
Q. I. WANG
Keyword(s):  
Lie Superalgebras ◽  
Maximal Subalgebras ◽  
Cartan Type

scholarly journals Tensor Hierarchy Algebra Extensions of Over-Extended Kac–Moody Algebras

2021 ◽  
Author(s):  
Martin Cederwall ◽  
Jakob Palmkvist
Keyword(s):  
Focus Of Attention ◽  
Lie Superalgebras ◽  
Algebraic Structures ◽  
Moody Algebra ◽  
Infinite Dimensional ◽  
Cartan Type ◽  
Fundamental Module

AbstractTensor hierarchy algebras are infinite-dimensional generalisations of Cartan-type Lie superalgebras. They are not contragredient, exhibiting an asymmetry between positive and negative levels. These superalgebras have been a focus of attention due to the fundamental rôle they play for extended geometry. In the present paper, we examine tensor hierarchy algebras which are super-extensions of over-extended (often, hyperbolic) Kac–Moody algebras. They contain novel algebraic structures. Of particular interest is the extension of a over-extended algebra by its fundamental module, an extension that contains and generalises the extension of an affine Kac–Moody algebra by a Virasoro derivation $$L_1$$ L 1 . A conjecture about the complete superalgebra is formulated, relating it to the corresponding Borcherds superalgebra.

scholarly journals Local superderivations on Cartan type Lie superalgebras

2021 ◽  
pp. 433-442
Author(s):  
Jixia Yuan ◽  
Liangyun Chen ◽  
Yan Cao
Keyword(s):  
Lie Superalgebras ◽  
Cartan Type
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