ترغب بنشر مسار تعليمي؟ اضغط هنا

Group gradings on filiform Lie algebras

142   0   0.0 ( 0 )
 نشر من قبل Elisabeth Remm
 تاريخ النشر 2013
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We classify, up to isomorphism, gradings by abelian groups on nilpotent filiform Lie algebras of nonzero rank. In case of rank 0, we describe conditions to obtain non trivial $Z_k$-gradings.



قيم البحث

اقرأ أيضاً

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically closed field of characteristic different from 2.
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.
215 - Eli Aljadeff , Ofir David 2014
We show that there exists a constant K such that for any PI- algebra W and any nondegenerate G-grading on W where G is any group (possibly infinite), there exists an abelian subgroup U of G with $[G : U] leq exp(W)^K$. A G-grading $W = bigoplus_{g in G}W_g$ is said to be nondegenerate if $W_{g_1}W_{g_2}... W_{g_r} eq 0$ for any $r geq 1$ and any $r$ tuple $(g_1, g_2,..., g_r)$ in $G^r$.
In this paper we consider gradings by a finite abelian group $G$ on the Lie algebra $mathfrak{sl}_n(F)$ over an algebraically closed field $F$ of characteristic different from 2 and not dividing $n$.
For any abelian group $G$, we classify up to isomorphism all $G$-gradings on the classical central simple Lie algebras, except those of type $D_4$, over the field of real numbers (or any real closed field).
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