اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدModular finite $W$-algebras
120
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $k$ be an algebraically closed field of characteristic $p > 0$ and let $G$ be a connected reductive algebraic group over $k$. Under some standard hypothesis on $G$, we give a direct approach to the finite $W$-algebra $U(mathfrak g,e)$ associated to a nilpotent element $e in mathfrak g = operatorname{Lie} G$. We prove a PBW theorem and deduce a number of consequences, then move on to define and study the $p$-centre of $U(mathfrak g,e)$, which allows us to define reduced finite $W$-algebras $U_eta(mathfrak g,e)$ and we verify that they coincide with those previously appearing in the work of Premet. Finally, we prove a modular version of Skryabins equivalence of categories, generalizing recent work of the second author.
قيم البحث
اقرأ أيضاً
Let $mathfrak g$ be a simple Lie algebra over $mathbb C$ and let $e in mathfrak g$ be nilpotent. We consider the finite $W$-algebra $U(mathfrak g,e)$ associated to $e$ and the problem of determining the variety $mathcal E(mathfrak g,e)$ of 1-dimensio
nal representations of $U(mathfrak g,e)$. For $mathfrak g$ of low rank, we report on computer calculations that have been used to determine the structure of $mathcal E(mathfrak g,e)$, and the action of the component group $Gamma_e$ of the centralizer of $e$ on $mathcal E(mathfrak g,e)$. As a consequence, we provide two examples where the nilpotent orbit of $e$ is induced, but there is a 1-dimensional $Gamma_e$-stable $U(mathfrak g,e)$-module which is not induced via Losevs parabolic induction functor. In turn this gives examples where there is a non-induced multiplicity free primitive ideal of $U(mathfrak g)$.
The $n$-slice algebra is introduced as a generalization of path algebra in higher dimensional representation theory. In this paper, we give a classification of $n$-slice algebras via their $(n+1)$-preprojective algebras and the trivial extensions of
their quadratic duals. One can always relate tame $n$-slice algebras to the McKay quiver of a finite subgroup of $mathrm{GL}(n+1, mathbb C)$. In the case of $n=2$, we describe the relations for the $2$-slice algebras related to the McKay quiver of finite Abelian subgroups of $mathrm{SL}(3, mathbb C)$ and of the finite subgroups obtained from embedding $mathrm{SL}(2, mathbb C)$ into $mathrm{SL}(3,mathbb C)$.
The objective of the present paper is to give a survey of recent progress on applications of the approaches of Ringel-Hall type algebras to quantum groups and cluster algebras via various forms of Greens formula. In this paper, three forms of Greens
formula are highlighted, (1) the original form of Greens formula cite{Green}cite{RingelGreen}, (2) the degeneration form of Greens formula cite{DXX} and (3) the projective form of Greens formula cite{XX2007a} i.e. Green formula with a $bbc^{*}$-action.
We study periodicity and twisted periodicity of the trivial extension algebra $T(A)$ of a finite-dimensional algebra $A$. We prove that (twisted) periodicity of the trivial extension is equivalent to $A$ being (twisted) fractionally Calabi--Yau. More
over, twisted periodicity of $T(A)$ is equivalent to the $d$-representation-finiteness of the $r$-fold trivial extension algebra $T_r(A)$ for some positive integers $r$ and $d$. These results allow us to construct a large number of new examples of periodic as well as fractionally Calabi--Yau algebras, and give answers to several open questions.
For each n>0, we define an algebra having many properties that one might expect to hold for a Brauer algebra of type Bn. It is defined by means of a presentation by generators and relations. We show that this algebra is a subalgebra of the Brauer alg
ebra of type Dn+1 and point out a cellular structure in it. This work is a natural sequel to the introduction of Brauer algebras of type Cn, which are subalgebras of classical Brauer algebras of type A2n-1 and differ from the current ones for n>2.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
