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Search Results: 1 - 10 of 80873 matches for " Wende Liu "
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Derivations from the even parts into the odd parts for Lie superalgebras W and S
Wende Liu,Baoling Liu
Mathematics , 2005,
Abstract: Let $\mathcal{W}$ and $\mathcal{S}$ denote the even parts of the general Witt superalgebra $W$ and the special superalgebra $S$ over a field of characteristic $ p>3,$ respectively. In this note, using the method of reduction on $\mathbb{Z}$-gradations, we determine the derivation space $\mathrm{Der}(\mathcal{W}, W_{\bar{1}})$ from $\mathcal{W}$ into $W_{\bar{1}} $ and the derivation space $\mathrm{Der}(\mathcal{S}, W_{\bar{1}})$ from $\mathcal{S}$ into $W_{\bar{1}}. $ In particular, the derivation space $\mathrm{Der}(\mathcal{S}, S_{\bar{1}})$ is determined.
Maximal graded subalgebras of Witt and Special superalgebras
Wende Liu,Xuan Liu
Mathematics , 2009,
Abstract: This paper has been withdrawn by the author due to that the main results and approaches are closedly parallel to the ones in Lie algebra case.
Generators of simple Lie superalgebras in characteristic 0
Wende Liu,Liming Tang
Physics , 2011,
Abstract: It is shown that any finite dimensional simple Lie superalgebra over an algebraically closed field of characteristic 0 is generated by 2 elements.
Generators of simple modular Lie superalgebras
Liming Tang,Wende Liu
Mathematics , 2012,
Abstract: Let $X$ be one of the finite-dimensional simple graded 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 also prove that certain classical Lie superalgebras or their relatives can be generated by one or two elements.
Maximal Subalgebras for Modular Graded Lie Superalgebras of Odd Cartan Type
Wende Liu,Qi Wang
Mathematics , 2013,
Abstract: The purpose of this paper is to determine all the maximal graded subalgebras of the four infinite families of finite-dimensional graded Lie superalgebras of odd Cartan type over an algebraically closed field of prime characteristic $p>3$. All the maximal graded subalgebras consist of three types (\MyRoman{1}), (\MyRoman{2}) and (\MyRoman{3}). In addition, the maximal graded subalgebras of type (\MyRoman{3}) consist of the maximal graded R-subalgebras and the maximal graded S-subalgebras. In this paper we classify all the maximal graded subalgebras for modular Lie superalgebras of odd Cartan type. We also determine the number of conjugacy classes, representatives of conjugacy classes and the dimensions for the maximal graded R-subalgebras and the maximal graded subalgebras of type (\MyRoman{2}). Here, determining the maximal graded S-subalgebras is reduced to determining the maximal subalgebras of classical Lie superalgebras $\mathfrak{p}(n)$.
Derivations for the even parts of modular Lie superalgebras $W$ and $S$ of Cartan type
Wende Liu,Yongzheng Zhang
Mathematics , 2005,
Abstract: Let $\mathbb{F}$ be the underlying base field of characteristic $p>3 $ and denote by $\mathcal{W}$ and $\mathcal{S}$ the even parts of the finite-dimensional generalized Witt Lie superalgebra $W$ and the special Lie superalgebra $S,$ respectively. We first give the generator sets of the Lie algebras $\mathcal{W}$ and $\mathcal{S}.$ Using certain properties of the canonical tori of $\mathcal{W}$ and $\mathcal{S},$ we then determine the derivation algebra of $\mathcal{W}$ and the derivation space of $\mathcal{S} $ to $\mathcal{W},$ where $\mathcal{W}$ is viewed as $\mathcal{S} $-module by means of the adjoint representation. As a result, we describe explicitly the derivation algebra of $\mathcal{S}.$ Furthermore, we prove that the outer derivation algebras of $\mathcal{W}$ and $\mathcal{S} $ are abelian Lie algebras or metabelian Lie algebras with explicit structure. In particular, we give the dimension formulae of the derivation algebras and outer derivation algebras of $\mathcal{W}$ and $\mathcal{S}.$ Thus we may make a comparison between the even parts of the (outer) superderivation algebras of $W$ and $S$ and the (outer) derivation algebras of the even parts of $W$ and $S,$ respectively.
Finite dimensional special odd contact superalgebras over a field of prime characteristic
Wende Liu,Jixia Yuan
Mathematics , 2009,
Abstract: This paper considers a family of finite dimensional simple Lie superalgebras of Cartan type over a field of characteristic $p>3$, the so-called special odd contact superalgebras. First, the spanning sets are determined for the Lie superalgebras and their relatives. Second, the spanning sets are used to characterize the simplicity and to compute the dimension formulas. Third, we determine the superderivation algebras and the first cohomology groups. Finally, the dimension formulas and the first cohomology groups are used to make a comparison between the special odd contact superalgebras and the other simple Lie superalgebras of Cartan type.
Filtration, automorphisms and classification of the infinite dimensional odd Contact superalgebras superalgebras
Jixia Yuan,Wende Liu
Mathematics , 2010, DOI: 10.1007/s11464-012-0185-6
Abstract: The principal filtration of the infinite-dimensional odd Contact Lie superalgebra over a field of characteristic $p>2$ is proved to be invariant under the automorphism group by investigating ad-nilpotent elements and determining certain invariants such as subalgebras generated by some ad-nilpotent elements. Then, it is proved that two automorphisms coincide if and only if they coincide on the -1 component with respect to the principal grading. Finally, all the odd Contact superalgebras are classified up to isomorphisms.
Restricted Kac modules of Hamiltonian Lie superalgebras of odd type
Jixia Yuan,Wende Liu
Mathematics , 2014,
Abstract: This paper aims to describe the restricted Kac modules of restricted Hamiltonian Lie superalgebras of odd type over an algebraically closed field of characteristic $p>3$. In particular, a sufficient and necessary condition for the restricted Kac modules to be irreducible is given in terms of typical weights.
The minimal number of generators for simple Lie superalgebras
Wende Liu,Liming Tang
Mathematics , 2012,
Abstract: Using the classification theorem due to Kac we prove that any finite dimensional simple Lie superalgebra over an algebraically closed field of characteristic 0 is generated by one element.
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