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.

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 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.

Automorphism groups of modular graded Lie superalgebras of Cartan-type

2017 ◽  
Vol 16 (03) ◽  
pp. 1750050
Author(s):  
Wende Liu ◽  
Jixia Yuan
Keyword(s):  
Automorphism Groups ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Infinite Dimensional ◽  
Cartan Type ◽  
Type Formula ◽  
Finite Dimensional ◽  
Normal Series

Suppose the underlying field is of characteristic [Formula: see text]. In this paper, we prove that the automorphisms of the finite-dimensional graded (non-restircited) Lie superalgebras of Cartan-type [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] can uniquely extend to the ones of the infinite-dimensional Lie superalgebra of Cartan-type [Formula: see text]. Then a concrete group embedding from [Formula: see text] into [Formula: see text] is established, where [Formula: see text] is any finite-dimensional Lie superalgebra of Cartan-type [Formula: see text] or [Formula: see text] and [Formula: see text] is the underlying (associative) superalgebra of [Formula: see text]. The normal series of the automorphism groups of [Formula: see text] are also considered.

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 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 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.

Inner structure in real vector spaces

2020 ◽  
Vol 27 (3) ◽  
pp. 361-366 ◽  
Author(s):  
Francisco Javier García-Pacheco ◽  
Enrique Naranjo-Guerra
Keyword(s):  
Convex Sets ◽  
Vector Spaces ◽  
Internal Point ◽  
Real Vector ◽  
Topological Vector Spaces ◽  
Infinite Dimensional ◽  
Intrinsic Characterization ◽  
The One ◽  
Locally Convex

AbstractInternal points were introduced in the literature of topological vector spaces to characterize the finest locally convex vector topology. In this manuscript we generalize the concept of internal point in real vector spaces by introducing a type of points, called inner points, that allows us to provide an intrinsic characterization of linear manifolds, which was not possible by using internal points. We also characterize infinite dimensional real vector spaces by means of the inner points of convex sets. Finally, we prove that in convex sets containing internal points, the set of inner points coincides with the one of internal points.

Automorphism Groups of Restricted Cartan-Type Lie Superalgebras

2006 ◽  
Vol 34 (10) ◽  
pp. 3767-3784 ◽  
Author(s):  
Wende Liu ◽  
Yongzheng Zhang
Keyword(s):  
Automorphism Groups ◽  
Lie Superalgebras ◽  
Cartan Type

FINITE-DIMENSIONAL SPECIAL ODD HAMILTONIAN SUPERALGEBRAS IN PRIME CHARACTERISTIC

2009 ◽  
Vol 11 (04) ◽  
pp. 523-546 ◽  
Author(s):  
WENDE LIU ◽  
YINGHUA HE
Keyword(s):  
Lie Superalgebras ◽  
The Other ◽  
Prime Characteristic ◽  
Characteristic P ◽  
Cartan Type ◽  
New Family ◽  
Finite Dimensional ◽  
Modular Lie Superalgebras

In this paper, we study a new family of finite-dimensional simple Lie superalgebras of Cartan type over a field of characteristic p > 3, the so-called special odd Hamiltonian superalgebras. The spanning sets are first given and then the grading structures are described explicitly. Finally, the simplicity and the dimension formulas are determined. As application, using the dimension formulas, we make a comparison between the special odd Hamiltonian superalgebras and the other known families of finite-dimensional simple modular Lie superalgebras of Cartan type.

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