ترغب بنشر مسار تعليمي؟ اضغط هنا

Graded Lie algebras of Cartan type in characteristic 2

389   0   0.0 ( 0 )
 نشر من قبل Tara Brough
 تاريخ النشر 2015
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We investigate the graded Lie algebras of Cartan type $W$, $S$ and $H$ in characteristic 2 and determine their simple constituents and some exceptional isomorphisms between them. We also consider the graded Lie algebras of Cartan type $K$ in characteristic 2 and conjecture that their simple constituents are isomorphic to Lie algebras of type $H$.



قيم البحث

اقرأ أيضاً

For a given abelian group G, we classify the isomorphism classes of G-gradings on the simple restricted Lie algebras of types W(m;1) and S(m;1) (m>=2), in terms of numerical and group-theoretical invariants. Our main tool is automorphism group scheme s, which we determine for the simple restricted Lie algebras of types S(m;1) and H(m;1). The ground field is assumed to be algebraically closed of characteristic p>3.
115 - Wende Liu , Qi Wang 2013
The purpose of this paper is to determine all maximal graded subalgebras of the four infinite series of finite-dimensional graded Lie superalgebras of odd Cartan type over an algebraically closed field of characteristic $p>3$. All maximal graded suba lgebras consist of three types (MyRoman{1}), (MyRoman{2}) and (MyRoman{3}). Maximal graded subalgebras of type (MyRoman{3}) fall into reducible maximal graded subalgebras and irreducible maximal graded subalgebras. In this paper we classify maximal graded subalgebras of types (MyRoman{1}), (MyRoman{2}) and reducible maximal g raded subalgebras.The classification of irreducible maximal graded subalgebras is reduced to that of the irreducible maximal subalgebras of the classical Lie superalgebra $mathfrak{p}(n)$.
In this paper we initiate the study of the maximal subalgebras of exceptional simple classical Lie algebras g over algebraically closed fields k of positive characteristic p, such that the prime characteristic is good for g. In this paper we deal wit h what is surely the most unnatural case; that is, where the maximal subalgebra in question is a simple subalgebra of non-classical type. We show that only the first Witt algebra can occur as a subalgebra of g and give explicit details on when it may be maximal in g.
We consider finite-dimensional irreducible transitive graded Lie algebras $L = sum_{i=-q}^rL_i$ over algebraically closed fields of characteristic three. We assume that the null component $L_0$ is classical and reductive. The adjoint representation o f $L$ on itself induces a representation of the commutator subalgebra $L_0$ of the null component on the minus-one component $L_{-1}.$ We show that if the depth $q$ of $L$ is greater than one, then this representation must be restricted.
Over an algebraically closed fields, an alternative to the method due to Kostrikin and Shafarevich was recently suggested. It produces all known simple finite dimensional Lie algebras in characteristic p>2. For p=2, we investigate one of the steps of this method, interpret several other simple Lie algebras, previously known only as sums of their components, as Lie algebras of vector fields. One new series of exceptional simple Lie algebras is discovered, together with its hidden supersymmetries. In characteristic 2, certain simple Lie algebras are desuperizations of simple Lie superalgebras. Several simple Lie algebras we describe as results of generalized Cartan prolongation of the non-positive parts, relative a simplest (by declaring degree of just one pair of root vectors corresponding to opposite simple roots nonzero) grading by integers, of Lie algebras with Cartan matrix are desuperizations of characteristic
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا