ترغب بنشر مسار تعليمي؟ اضغط هنا

On nilpotent generators of the symplectic Lie algebra

68   0   0.0 ( 0 )
 نشر من قبل Alisa Chistopolskaya
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

Let $mathfrak{sp}_{2n}(mathbb {K})$ be the symplectic Lie algebra over an algebraically closed field of characteristic zero. We prove that for any nonzero nilpotent element $X in mathfrak{sp}_{2n}(mathbb {K})$ there exists a nilpotent element $Y in mathfrak{sp}_{2n}(mathbb {K})$ such that $X$ and $Y$ generate $mathfrak{sp}_{2n}(mathbb {K})$.



قيم البحث

اقرأ أيضاً

Consider the special linear Lie algebra $mathfrak{sl}_n(mathbb {K})$ over an infinite field of characteristic different from $2$. We prove that for any nonzero nilpotent $X$ there exists a nilpotent $Y$ such that the matrices $X$ and $Y$ generate the Lie algebra $mathfrak{sl}_n(mathbb {K})$.
We study symplectic structures on nilpotent Lie algebras. Since the classification of nilpotent Lie algebras in any dimension seems to be a crazy dream, we approach this study in case of 2-step nilpotent Lie algebras (in this sub-case also, the class ification fo the dimension greater than 8 seems very difficult), using not a classification but a description of subfamilies associated with the characteristic sequence. We begin with the dimension $8$, first step where the classification becomes difficult.
The classification of complex of real finite dimensional Lie algebras which are not semi simple is still in its early stages. For example the nilpotent Lie algebras are classified only up to the dimension 7. Moreover, to recognize a given Lie algebra in a classification list is not so easy. In this work we propose a different approach to this problem. We determine families for some fixed invariants, the classification follows by a deformation process or contraction process. We focus on the case of 2 and 3-step nilpotent Lie algebras. We describe in both cases a deformation cohomology of this type of algebras and the algebras which are rigid regarding this cohomology. Other $p$-step nilpotent Lie algebras are obtained by contraction of the rigid ones.
72 - Wende Liu , Yong Yang , 2018
In this paper, we study the cup products and Betti numbers over cohomology superspaces of two-step nilpotent Lie superalgebras with coefficients in the adjoint modules over an algebraically closed field of characteristic zero. As an application, we p rove that the cup product over the adjoint cohomology superspaces for Heisenberg Lie superalgebras is trivial and we also determine the adjoint Betti numbers for Heisenberg Lie superalgebras by means of Hochschild-Serre spectral sequences.
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