اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدClassifications of some classes of Zinbiel algebras
148
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this work nul-filiform and filiform Zinbiel algebras are described up to isomorphism. Moreover, the classification of complex Zinbiel algebras is extended from dimensions $leq 3$ up to the dimension $4.$
قيم البحث
اقرأ أيضاً
We describe all central extensions of all $3$-dimensional non-zero complex Zinbiel algebras. As a corollary, we have a full classification of $4$-dimensional non-trivial complex Zinbiel algebras and a full classification of $5$-dimensional non-trivia
l complex Zinbiel algebras with $2$-dimensional annihilator, which gives the principal step in the algebraic classification of $5$-dimensional Zinbiel algebras.
In this work the description up to isomorphism of complex naturally graded quasi-filiform Zinbiel algebras is obtained.
We present the classification of a subclass of $n$-dimensional naturally graded Zinbiel algebras. This subclass has the nilindex $n-3$ and the characteristic sequence $(n-3,2,1).$ In fact, this result completes the classification of naturally graded Zinbiel algebras of nilindex $n-3.$
In this paper, by using the Composition-Diamond lemma for non-associative algebras invented by A. I. Shirshov in 1962, we give Gr{o}bner-Shirshov bases for free Pre-Lie algebras and the universal enveloping non-associative algebra of an Akivis algebr
a, respectively. As applications, we show I.P. Shestakovs result that any Akivis algebra is linear and D. Segals result that the set of all good words in $X^{**}$ forms a linear basis of the free Pre-Lie algebra $PLie(X)$ generated by the set $X$. For completeness, we give the details of the proof of Shirshovs Composition-Diamond lemma for non-associative algebras.
In this paper we prove that any local automorphism on the solvable Leibniz algebras with null-filiform and naturally graded non-Lie filiform nilradicals, whose dimension of complementary space is maximal is an automorphism. Furthermore, the same prob
lem concerning 2-local automorphisms of such algebras is investigated and we obtain the analogously results for 2-local automorphisms.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
