Some examples of nil Lie algebras
Generalizing Petrogradsky’s construction, we give examples of infinite-dimensional nil Lie algebras of finite Gelfand–Kirillov dimension over any field of positive characteristic.
Some necessary and sufficient conditions for nilpotent -Lie superalgebras
The paper studies nilpotent -Lie superalgebras over a field of characteristic zero. More specifically speaking, we prove Engel’s theorem for -Lie superalgebras which is a generalization of those for -Lie algebras and Lie superalgebras. In addition, as an application of Engel’s theorem, we give some properties of nilpotent -Lie superalgebras and obtain several sufficient conditions for an -Lie superalgebra to be nilpotent by using the notions of the maximal subalgebra, the weak ideal and the...
Some notes about -Lie algebras.
Some properties of generalized reduced Verma modules over -graded modular Lie superalgebras
We study some properties of generalized reduced Verma modules over -graded modular Lie superalgebras. Some properties of the generalized reduced Verma modules and coinduced modules are obtained. Moreover, invariant forms on the generalized reduced Verma modules are considered. In particular, for -graded modular Lie superalgebras of Cartan type we prove that generalized reduced Verma modules are isomorphic to mixed products of modules.
Some properties of the family of modular Lie superalgebras
In this paper, we continue to investigate some properties of the family of finite-dimensional simple modular Lie superalgebras which were constructed by X. N. Xu, Y. Z. Zhang, L. Y. Chen (2010). For each algebra in the family, a filtration is defined and proved to be invariant under the automorphism group. Then an intrinsic property is proved by the invariance of the filtration; that is, the integer parameters in the definition of Lie superalgebras are intrinsic. Thereby, we classify these Lie...
Spectral sequences for commutative Lie algebras
We construct some spectral sequences as tools for computing commutative cohomology of commutative Lie algebras in characteristic . In a first part, we focus on a Hochschild-Serre-type spectral sequence, while in a second part we obtain spectral sequences which compare Chevalley-Eilenberg-, commutative- and Leibniz cohomology. These methods are illustrated by a few computations.
Support varieties for restricted Lie alge-bras.
The classification of modular Lie superalgebras of type M
The 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.
The finite dimension property of the irreducible representations of Noetherian -Lie algebras.
Troisième théorème fondamental de réalisation de Cartan
De même qu’avec les groupes de Lie, à tout pseudo-groupe infinitésimal de Lie sur il est associé de façon naturelle une algèbre de Lie , qui est une sous-algèbre de Lie fermée de l’algèbre de Lie de tous les champs de vecteurs formels de , l’algèbre étant munie de la topologie définie par la filtration naturelle de l’algèbre des séries formelles. Le troisième théorème fondamental de Cartan dit qu’inversement étant donnée une sous-algèbre de Lie transitive fermée de l’algèbre , il existe...
Une théorie algébrique des bases et familles basiques des algèbres de Lie libres
Абелевы расширения модулярных алгебр Ли
Алгебраические группы, ассоциированные с картановскими p-алгебрами Ли
Алгебры Ли без сильного вырождения
Алгебры Ли с конечной градуировкой
Градуированные алгебры Ли с нулевой компонентой, равной сумме коммутурующих идеалов
Деформации алгебр Ли
Замечание к статье С.П.Демушкина "Подалгебры Картана простых p-алгебр Ли and
Индексы стандартных максимальных подалгебр p-алгебр картановского типа конечной характеристики
Классификация гамильтоновых форм над алгебрами разделенных степеней