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

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.

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 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 Superderivations for Modular Graded Lie Superalgebras of Cartan-type

2012 ◽  
Vol 17 (1) ◽  
pp. 69-86 ◽  
Author(s):  
Wei Bai ◽  
Wende Liu
Keyword(s):  
Lie Superalgebras ◽  
Cartan Type

scholarly journals Generators of Simple Modular Lie Superalgebras

2016 ◽  
Vol 23 (02) ◽  
pp. 347-360
Author(s):  
Liming Tang ◽  
Wende Liu
Keyword(s):  
Lie Superalgebras ◽  
Closed Field ◽  
Characteristic P ◽  
Algebraically Closed Field ◽  
Cartan Type ◽  
Finite Dimensional ◽  
Modular Lie Superalgebras

Let X be one of the finite-dimensional graded simple Lie superalgebras of Cartan type W, S, H, K, HO, KO, SHO or SKO over an algebraically closed field of characteristic p > 3. In this paper we prove that X can be generated by one element except the ones of type W, HO, KO or SKO in certain exceptional cases in which X can be generated by two elements. As a subsidiary result, we prove that certain classical Lie superalgebras or their relatives can be generated by one or two elements.

On Blocks in Restricted Representations of Lie Superalgebras of Cartan Type

2020 ◽  
Vol 36 (9) ◽  
pp. 1061-1075
Author(s):  
Fei Fei Duan ◽  
Bin Shu ◽  
Yu Feng Yao
Keyword(s):  
Lie Superalgebras ◽  
Cartan Type
Sign in / Sign up

Export Citation Format

Share Document