The Cartan-Type Modular Lie Superalgebra<i>KO</i>

Fu, Jiang; Zhang, Qingcheng; Jiang, Cuipo

doi:10.1080/00927870500346065

Cited by 29 publications

(90 citation statements)

References 9 publications

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“…is a finite-dimensional simple subalgebra of W (n, n + 1; t), known as the odd contact Lie superalgebra (see [4]). The even part of this Lie superalgebra is called the odd contact Lie algebra, denoted by K(n, n + 1; t).…”

Section: Notation and Main Resultsmentioning

confidence: 99%

“…Recently, one can also find work on the representations of the classical modular Lie superalgebras (see, for example, [14,15]). For the simple modular Lie algebras and simple modular Lie superalgebras of Cartan type, the (super)derivation algebras have been sufficiently studied (for example, see [3,4,8,9,10,11,12,13]). In [4,11], the superderivation algebras of Lie superalgebras of Cartan-type H, W , S, K, HO and KO were determined.…”

Section: Introductionmentioning

confidence: 99%

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Derivations of the Odd Contact Lie Algebras in Prime Characteristic

Cao¹,

Sun²,

Yuan³

2013

Journal of the Korean Mathematical Society

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Abstract. The underlying field is of characteristic p > 2. In this paper, we first use the method of computing the homogeneous derivations to determine the first cohomology of the so-called odd contact Lie algebra with coefficients in the even part of the generalized Witt Lie superalgebra. In particular, we give a generating set for the Lie algebra under consideration. Finally, as an application, the derivation algebra and outer derivation algebra of the Lie algebra are completely determined. IntroductionIn this paper, we consider a family of non-simple modular Lie algebras, called the odd contact Lie algebras, which are actually the even parts of the odd contact simple Lie superalgebras that are also closely related to the contact simple Lie algebras. The main purpose is to compute the first cohomology of the odd contact Lie algebras with coefficients in their adjoint representations. In other words, we determine the derivation algebras and the outer derivation algebras.As is well-known, the theory of modular Lie algebras has undergone a remarkable evolution. In the super-case, the theory of modular Lie superalgebras has also obtained many interesting results in the past decade. For example, one can find work on the classification of classical modular Lie superalgebras [1, 2] and on the structures and representations of modular Lie superalgebras of Cartan type [6,7,9,16,17,18]. Recently, one can also find work on the representations of the classical modular Lie superalgebras (see, for example, [14,15]). For the simple modular Lie algebras and simple modular Lie superalgebras of Cartan type, the (super)derivation algebras have been sufficiently studied (for example, see [3,4,8,9,10,11,12,13]). In [4,11], the superderivation algebras of Lie superalgebras of Cartan-type H, W , S, K, HO and KO were determined. For the derivations of the even parts of Lie superalgebras

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Section: Notation and Main Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Derivations of the Odd Contact Lie Algebras in Prime Characteristic

Cao¹,

Sun²,

Yuan³

2013

Journal of the Korean Mathematical Society

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“…By means of [13,19], we see that the dimension of modular Lie superalgebras HO is odd and the dimension of modular Lie superalgebras H can not be divided by p. So O is not isomorphic to modular Lie superalgebras H and HO, respectively. The outer derivations of W , S, K and KO are all ad-nilpotent in [6,23], but O possesses outer derivations D θ which are not ad-nilpotent. It follows that O is not isomorphic to modular Lie superalgebras W , S, K and KO, respectively.…”

Section: Lemma 47 Let T > 2 and ϕ ∈ H(dermentioning

confidence: 99%

Superderivation algebras of modular Lie superalgebras of O-type

2015

Chin. Ann. Math. Ser. B

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The authors consider a family of finite-dimensional Lie superalgebras of O-type over an algebraically closed field of characteristic p > 3. It is proved that the Lie superalgebras of O-type are simple and the spanning sets are determined. Then the spanning sets are employed to characterize the superderivation algebras of these Lie superalgebras. Finally, the associative forms are discussed and a comparison is made between these Lie superalgebras and other simple Lie superalgebras of Cartan type.

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“…Then Q(m) has an F-basis {y λ | λ ∈ H}. The tensor product [3] The generalized Witt modular Lie superalgebra 147…”

Section: Basics and Constructionmentioning

confidence: 99%

“…Due to the prime characteristic and superstructure of Lie superalgebras, their derivation superalgebras are harder to determine. Despite this, the derivation superalgebras of W, S , H, K, HO and KO have been determined (see [3,7,8,12,15]). …”

Section: Introductionmentioning

confidence: 99%