Finite-dimensional Lie superalgebras of Cartan type over fields of prime characteristic

1997 ◽  
Vol 42 (9) ◽  
pp. 720-724 ◽  
Author(s):  
Yongzheng Zhang
Keyword(s):  
Lie Superalgebras ◽  
Prime Characteristic ◽  
Cartan Type ◽  
Finite Dimensional

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.

A Class of Finite-dimensional Lie Superalgebras of Hamiltonian Type

2011 ◽  
Vol 18 (02) ◽  
pp. 347-360 ◽  
Author(s):  
Li Ren ◽  
Qiang Mu ◽  
Yongzheng Zhang
Keyword(s):  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Prime Characteristic ◽  
Cartan Type ◽  
Finite Dimensional ◽  
Derivation Superalgebra

A class of finite-dimensional Cartan-type Lie superalgebras H(n,m) over a field of prime characteristic is studied in this paper. We first determine the derivation superalgebra of H(n,m). Then we obtain that H(n,m) is restrictable and it is an extension of the Lie superalgebra [Formula: see text]. Finally, we prove that H(n,m) is isomorphic to a subalgebra of the restricted Hamiltonian Lie superalgebra [Formula: see text].

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 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.

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.

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.

Automorphisms and p-Characters of Restricted Lie Superalgebras of Cartan Type

2011 ◽  
Vol 18 (03) ◽  
pp. 397-410 ◽  
Author(s):  
Jixia Yuan ◽  
Yan Chen ◽  
Wende Liu
Keyword(s):  
Automorphism Group ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Irreducible Representations ◽  
Prime Characteristic ◽  
Cartan Type ◽  
Restricted Lie Superalgebra ◽  
Normal Series ◽  
Standard Normal

Let X be a restricted Lie superalgebra of Cartan type W, S, H or K over a field of prime characteristic. In this paper, we describe the quotients of the standard normal series of the automorphism group of X. As an application, the results above are used to discuss the p-characters of the irreducible representations for X.

scholarly journals Maximal subalgebras for Lie superalgebras of Cartan type

2014 ◽  
Vol 14 (02) ◽  
pp. 1550013 ◽  
Author(s):  
Wei Bai ◽  
Wende Liu ◽  
Xuan Liu ◽  
Hayk Melikyan
Keyword(s):  
Lie Superalgebras ◽  
Constructive Method ◽  
Prime Characteristic ◽  
Maximal Subalgebras ◽  
Cartan Type ◽  
Isomorphism Classes

The maximal graded subalgebras for four families of Lie superalgebras of Cartan type over a field of prime characteristic are studied. All maximal graded subalgebras are described completely by a constructive method and their isomorphism classes, dimension formulas are found except for maximal irreducible graded subalgebras. The classification of maximal irreducible graded subalgebras is reduced to the classification of the maximal irreducible subalgebras for the classical Lie superalgebras 𝔤𝔩(m, n), 𝔰𝔩(m, n) and 𝔬𝔰𝔭(m, n).

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