اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the lower central series of an associative algebra
123
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
This paper continues the study of the lower central series quotients of an associative algebra A, regarded as a Lie algebra, which was started in math/0610410 by Feigin and Shoikhet. Namely, it provides a basis for the second quotient in the case when A is the free algebra in n generators (note that the Hilbert series of this quotient was determined earlier in math/0610410). Further, it uses this basis to determine the structure of the second quotient in the case when A is the free algebra modulo the relations saying that the generators have given nilpotency orders. Finally, it determines the structure of the third and fourth quotient in the case of 2 generators, confirming an answer conjectured in math/0610410. Finally, in the appendix, the results of math/0610410 are generalized to the case when A is an arbitrary associative algebra (under certain conditions on $A$).
قيم البحث
اقرأ أيضاً
Given a symmetric operad $mathcal{P}$ and a $mathcal{P}$-algebra $V$, the associative universal enveloping algebra ${mathsf{U}_{mathcal{P}}}$ is an associative algebra whose category of modules is isomorphic to the abelian category of $V$-modules. We
study the notion of PBW property for universal enveloping algebras over an operad. In case $mathcal{P}$ is Koszul a criterion for the PBW property is found. A necessary condition on the Hilbert series for $mathcal{P}$ is discovered. Moreover, given any symmetric operad $mathcal{P}$, together with a Grobner basis $G$, a condition is given in terms of the structure of the underlying trees associated with leading monomials of $G$, sufficient for the PBW property to hold. Examples are provided.
Every irreducible finite-dimensional representation of the quantized enveloping algebra U_q(gl_n) can be extended to the corresponding quantum affine algebra via the evaluation homomorphism. We give in explicit form the necessary and sufficient condi
tions for irreducibility of tensor products of such evaluation modules.
We study monoidal categorifications of certain monoidal subcategories $mathcal{C}_J$ of finite-dimensional modules over quantum affine algebras, whose cluster algebra structures coincide and arise from the category of finite-dimensional modules over
quiver Hecke algebra of type A${}_infty$. In particular, when the quantum affine algebra is of type A or B, the subcategory coincides with the monoidal category $mathcal{C}_{mathfrak{g}}^0$ introduced by Hernandez-Leclerc. As a consequence, the modules corresponding to cluster monomials are real simple modules over quantum affine algebras.
In this paper the W-algebra W(2,2) and its representation theory are studied. It is proved that a simple vertex operator algebra generated by two weight 2 vectors is either a vertex operator algebra associated to a highest irreducible W(2,2)-module o
r a tensor product of two irreducible Virasoro vertex operator algebras. Furthermore, any rational, C_2-cofinite simple vertex operator algebra whose weight 1 subspace is zero and weight 2 subspace is 2-dimensional, and with central charge c=1 is isomorphic to L(1/2,0)otimes L(1/2,0).
We propose a quantum analogue of a Tits-Kantor-Koecher algebra with a Jordan torus as an coordinated algebra by looking at the vertex operator construction over a Fock space.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
