ترغب بنشر مسار تعليمي؟ اضغط هنا

The algebraic and geometric classification of nilpotent right alternative algebras

61   0   0.0 ( 0 )
 نشر من قبل Ivan Kaygorodov
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We present algebraic and geometric classifications of the $4$-dimensional complex nilpotent right alternative algebras. Specifically, we find that, up to isomorphism, there are only $9$ non-isomorphic nontrivial nilpotent right alternative algebras. The corresponding geometric variety has dimension $13$ and it is determined by the Zariski closure of $4$ rigid algebras and one one-parametric family of algebras.



قيم البحث

اقرأ أيضاً

We give the complete algebraic classification of all complex 4-dimensional nilpotent algebras. The final list has 234 (parametric families of) isomorphism classes of algebras, 66 of which are new in the literature.
An algebraic classification of complex $5$-dimensional nilpotent commutative $mathfrak{CD}$-algebras is given. This classification is based on an algebraic classification of complex $5$-dimensional nilpotent Jordan algebras.
We give a geometric classification of complex $n$-dimensional $2$-step nilpotent (all, commutative and anticommutative) algebras. Namely, has been found the number of irreducible components and their dimensions. As a corollary, we have a geometric cl assification of complex $5$-dimensional nilpotent associative algebras. In particular, it has been proven that this variety has $14$ irreducible components and $9$ rigid algebras.
In this paper we investigate the derivations of filiform Leibniz algebras. Recall that the set of filiform Leibniz algebras of fixed dimension is decomposed into three non-intersected families. We found sufficient conditions under which filiform Leib niz algebras of the first family are characteristically nilpotent. Moreover, for the first family we classify non-characteristically nilpotent algebras by means of Catalan numbers. In addition, for the rest two families of filiform Leibniz algebras we describe non-characteristically nilpotent algebras, i.e., those filiform Leibniz algebras which lie in the complementary set to those characteristically nilpotent.
107 - Elisabeth Remm 2017
A finite dimensional filiform K-Lie algebra is a nilpotent Lie algebra g whose nil index is maximal, that is equal to dim g -1. We describe necessary and sufficient conditions for a filiform algebra over an algebraically closed field of characteristi c 0 to admit a contact linear form (in odd dimension) or a symplectic structure (in even dimension). If we fix a Vergnes basis, the set of filiform n-dimensional Lie algebras is a closed Zariski subset of an affine space generated by the structure constants associated with this fixed basis. Then this subset is an algebraic variety and we describe in small dimensions the algebraic components.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا