ترغب بنشر مسار تعليمي؟ اضغط هنا

Groebner-Shirshov Bases for Associative Algebras with Multiple Operators and Free Rota-Baxter Algebras

191   0   0.0 ( 0 )
 نشر من قبل Yuqun Chen
 تاريخ النشر 2009
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper, we establish the Composition-Diamond lemma for associative algebras with multiple linear operators. As applications, we obtain Groebner-Shirshov bases of free Rota-Baxter algebra, $lambda$-differential algebra and $lambda$-differential Rota-Baxter algebra, respectively. In particular, linear bases of these three free algebras are respectively obtained, which are essentially the same or similar to those obtained by Ebrahimi-Fard and Guo, and Guo and Keigher recently by using other methods.



قيم البحث

اقرأ أيضاً

In this paper, we obtain respectively some new linear bases of free unitary (modified) weighted differential algebras and free nonunitary (modified) Rota-Baxter algebras, in terms of the method of Gr{o}bner-Shirshov bases.
176 - L. A. Bokut , Yuqun Chen 2008
In this paper, we review Shirshovs method for free Lie algebras invented by him in 1962 which is now called the Groebner-Shirshov bases theory.
128 - Maxim Goncharov 2020
We generalize the notion of a Rota-Baxter operator on groups and the notion of a Rota-Baxter operator of weight 1 on Lie algebras and define and study the notion of a Rota-Baxter operator on a cocommutative Hopf algebra $H$. If $H=F[G]$ is the group algebra of a group $G$ or $H=U(mathfrak{g})$ the universal enveloping algebra of a Lie algebra $mathfrak{g}$, then we prove that Rota-Baxter operators on $H$ are in one to one correspondence with corresponding Rota-Baxter operators on groups or Lie algebras.
We give the description of homogeneous Rota-Baxter operators, Reynolds operators, Nijenhuis operators, Average operators and differential operator of weight 1 of null-filiform associative algebras of arbitrary dimension.
109 - Apurba Das , Shuangjian Guo 2021
In this paper, we introduce twisted relative Rota-Baxter operators on a Leibniz algebra as a generalization of twisted Poisson structures. We define the cohomology of a twisted relative Rota-Baxter operator $K$ as the Loday-Pirashvili cohomology of a certain Leibniz algebra induced by $K$ with coefficients in a suitable representation. Then we consider formal deformations of twisted relative Rota-Baxter operators from cohomological points of view. Finally, we introduce and study NS-Leibniz algebras as the underlying structure of twisted relative Rota-Baxter operators.
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