scholarly journals The classification of modular Lie superalgebras of type M

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Lili Ma ◽  
Liangyun Chen
Keyword(s):  
Intrinsic Property ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Characteristic P ◽  
Infinite Dimensional ◽  
Modular Lie Superalgebra ◽  
Nilpotent Elements ◽  
Natural Filtration ◽  
Modular Lie Superalgebras

AbstractThe natural filtration of the infinite-dimensional simple modular Lie superalgebra M over a field of characteristic p > 2 is proved to be invariant under automorphisms by discussing ad-nilpotent elements. Moreover, an intrinsic property is obtained and all the infinite-dimensional simple modular Lie superalgebras M are classified up to isomorphisms. As an application, a property of automorphisms of M is given.

scholarly journals Infinite-Dimensional Modular Lie SuperalgebraΩ

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Xiaoning Xu ◽  
Bing Mu
Keyword(s):  
Positive Characteristic ◽  
Intrinsic Property ◽  
Lie Superalgebra ◽  
Infinite Dimensional ◽  
Modular Lie Superalgebra ◽  
Nilpotent Elements ◽  
Natural Filtration ◽  
Definition Of ◽  
Field Of Positive Characteristic

All ad-nilpotent elements of the infinite-dimensional Lie superalgebraΩover a field of positive characteristic are determined. The natural filtration of the Lie superalgebraΩis proved to be invariant under automorphisms by characterizing ad-nilpotent elements. Then an intrinsic property is obtained by the invariance of the filtration; that is, the integers in the definition ofΩare intrinsic. Therefore, we classify the infinite-dimensional modular Lie superalgebraΩin the sense of isomorphism.

scholarly journals The Natural Filtration of Finite Dimensional Modular Lie Superalgebras of Special Type

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Keli Zheng ◽  
Yongzheng Zhang
Keyword(s):  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Prime Characteristic ◽  
Modular Lie Superalgebra ◽  
Finite Dimensional ◽  
Natural Filtration ◽  
Modular Lie Superalgebras

This paper is concerned with the natural filtration of Lie superalgebraS(n,m)of special type over a field of prime characteristic. We first construct the modular Lie superalgebraS(n,m). Then we prove that the natural filtration ofS(n,m)is invariant under its automorphisms.

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 Natural Filtrations of Infinite-Dimensional Modular Contact Superalgebras

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Qiang Mu
Keyword(s):  
Positive Characteristic ◽  
Lie Superalgebras ◽  
Closed Field ◽  
Infinite Dimensional ◽  
Intrinsic Characterization ◽  
Nilpotent Elements ◽  
Natural Filtration ◽  
Field Of Positive Characteristic

The natural filtration of the infinite-dimensional contact superalgebra over an algebraic closed field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent elements and the subalgebras generated by certain ad-nilpotent elements. Moreover, we obtain an intrinsic characterization of contact superalgebras and a property of automorphisms of these Lie superalgebras.

scholarly journals REPRESENTATIONS OF THE EXCEPTIONAL LIE SUPERALGEBRA E(3,6) III: CLASSIFICATION OF SINGULAR VECTORS

2005 ◽  
Vol 04 (01) ◽  
pp. 15-57 ◽  
Author(s):  
VICTOR G. KAC ◽  
ALEXEI RUDAKOV
Keyword(s):  
Vector Fields ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Irreducible Representations ◽  
Verma Modules ◽  
Locally Finite ◽  
Infinite Dimensional ◽  
Singular Vectors ◽  
Zero Degree

We continue the study of irreducible representations of the exceptional Lie superalgebra E(3,6). This is one of the two simple infinite-dimensional Lie superalgebras of vector fields which have a Lie algebra sℓ(3) × sℓ(2) × gℓ(1) as the zero degree component of its consistent ℤ-grading. We provide the classification of the singular vectors in the degenerate Verma modules over E(3,6), completing thereby the classification and construction of all irreducible E(3,6)-modules that are L0-locally finite.

Infinite-dimensional Modular Lie Superalgebras W and S of Cartan Type

2006 ◽  
Vol 13 (02) ◽  
pp. 197-210 ◽  
Author(s):  
Yongzheng Zhang ◽  
Wende Liu
Keyword(s):  
Automorphism Groups ◽  
Lie Superalgebras ◽  
Infinite Dimensional ◽  
Cartan Type ◽  
Intrinsic Characterization ◽  
Nilpotent Elements ◽  
Modular Lie Superalgebras

The natural filtrations of infinite-dimensional modular Lie superalgebras W and S are proved to be invariant under their automorphism groups by means of investigating the ad-nilpotent elements and determining certain subalgebras generated by ad-nilpotent elements. As an application, we obtain an intrinsic characterization of W and S, and give a property of the automorphisms of these modular Lie superalgebras.

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 Equivariant Map Queer Lie Superalgebras

2016 ◽  
Vol 68 (2) ◽  
pp. 258-279 ◽  
Author(s):  
Lucas Calixto ◽  
Adriano Moura ◽  
Alistair Savage
Keyword(s):  
Finite Group ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Equivariant Map ◽  
Isomorphism Classes ◽  
Finite Dimensional ◽  
Regular Maps ◽  
A Finite Group ◽  
Special Case

AbstractAn equivariant map queer Lie superalgebra is the Lie superalgebra of regular maps from an algebraic variety (or scheme) X to a queer Lie superalgebra q that are equivariant with respect to the action of a finite group Γ acting on X and q. In this paper, we classify all irreducible finite-dimensional representations of the equivariant map queer Lie superalgebras under the assumption that Γ is abelian and acts freely on X. We show that such representations are parameterized by a certain set of Γ-equivariant finitely supported maps from X to the set of isomorphism classes of irreducible finite-dimensional representations of q. In the special case where X is the torus, we obtain a classification of the irreducible finite-dimensional representations of the twisted loop queer superalgebra.

QUANTIZATION AND COCYCLES ON THE SUPERTORUS AND LARGE-N LIMITS FOR THE CLASSICAL LIE SUPERALGEBRAS

1991 ◽  
Vol 06 (03) ◽  
pp. 217-224 ◽  
Author(s):  
E.S. FRADKIN ◽  
V. Ya. LINETSKY
Keyword(s):  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Infinite Dimensional ◽  
Large N

The Poisson superbracket Lie superalgebra on the supertorus T2d|N is considered and its quantization is carried out. It is shown that there exists a non-trivial supercentral extension by means of 2d arbitrary c-numbers (when N is even), or 2d Grassmann numbers (when N is odd). It is shown that the infinite-dimensional superalgebras on the supertorus T2d|N can be considered as certain generalizations and large-M limits of the classical superalgebras A(M| M) and Q(M) (when N is even and odd respectively).

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