共查询到20条相似文献,搜索用时 15 毫秒
1.
We propose a construction of the spherical subalgebra of a symplectic reection algebra of an arbitrary rank corresponding to a star-shaped affine Dynkin diagram. Namely, it is obtained from the universal enveloping algebra of a certain semisimple Lie algebra by the process of quantum Hamiltonian reduction. As an application, we propose a construction of finite-dimensional representations of the spherical subalgebra. 相似文献
2.
Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras (Sym(N))N≥1, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N=1 and N=2). We compute their Hilbert series, introduce and study several combinatorial bases, and establish various algebraic identities
related to the multisection of formal power series with noncommutative coefficients.
Received November 19, 2004 相似文献
3.
A. Fošner 《Ukrainian Mathematical Journal》2018,69(10):1659-1667
4.
设N是Banach空间X上的套,AlgN是相应的套代数。本文证明了,若套N中存在一个非平凡元在X中可补,那么AlgN上的每个可加Jordan高阶导子和每个可加三重Jordan高阶导子都是高阶导子。 相似文献
5.
Let N be a nest on a Banach space X, and Alg N be the associated nest algebra. It is shown that if there exists a non-trivial element in N which is complemented in X, then D = (Ln)n∈N is a Lie higher derivation of AlgAl if and only if each Ln has the form Ln(A) : Tn(A) + hn(A)I for all A ∈ AlgN, where (Tn)n∈N is a higher derivation and (hn)n∈N is a sequence of additive functionals satisfying hn([A,B]) = 0 for all A,B ∈ AlgN and all n ∈ N. 相似文献
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7.
Philippe Revoy 《Advances in Applied Clifford Algebras》2014,24(1):205-212
The aim of this lecture is to introduce Clifford algebras of polynomial forms of higher degrees. We recall that these algebras are in general of infinite dimension, and we give a basis depending on a given basis of the underlying vector space. We then show that, though they contain large free associative algebras, we may construct finite dimensional representations of these algebras, also called linearizations of the polynomial form. If the polynomial form is, in a certain sense, non degenerate, the dimensions of these representations are multiples of the degree of the form. In the end, we recall some results known for the special case of a binary cubic form with at least one simple zero, when explicit computations can be done: the Clifford algebra is an Azumaya algebra of rank 9 over its center, which is the algebra of functions over a cubic curve depending on the given cubic form. 相似文献
8.
In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algeb... 相似文献
9.
One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the
Gray tensor product. In this paper we begin to adapt the machinery of globular operads (Batanin, Adv Math 136:39–103, 1998) to this task. We present a general construction of a tensor product on the category of n-globular sets from any normalised (n + 1)-operad A, in such a way that the algebras for A may be recaptured as enriched categories for the induced tensor product. This is an important step in reconciling the globular
and simplicial approaches to higher category theory, because in the simplicial approaches one proceeds inductively following
the idea that a weak (n + 1)-category is something like a category enriched in weak n-categories. In this paper we reveal how such an intuition may be formulated in terms of globular operads. 相似文献
10.
In this paper,we will give the definition of completable nilpotent Lie algebras,discuss its decomposition and prove that the heisenberg algebras and extensions of abelian quadratic Lie algebras are all completable nilpotent Lie algebras. 相似文献
11.
It is shown that if is an infinite, metrizable, compact spacesuch that some finite order iterated derived set of is empty,then dgC()=dbC()=2. 2000 Mathematics Subject Classification46M20 (primary), 46J10 (secondary). 相似文献
12.
两类新的loop代数及其应用 总被引:1,自引:0,他引:1
利用构造的两类特殊 loop代数 ,建立了线性等谱问题 .作为应用 ,求得了著名的 Kd V方程族和 Tu方程族的可积耦合系统 .这种方法可以普遍地应用 相似文献
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14.
The purpose of this note is to obtain precise information about associative or Jordan algebras generated by two idempotents. 相似文献
15.
Kyungyong Lee 《Annals of Combinatorics》2012,16(2):305-317
In this note, we find an explicit formula for the Laurent expression of cluster variables of coefficient-free rank two cluster algebras associated with the matrix ${{\left(\begin{array}{ll} 0 &c \\ -c &0 \end{array}\right)}}$ , which manifestly shows that a large number of coefficients are non-negative. As a corollary, we obtain an explicit expression for the Euler-Poincaré characteristics of the corresponding quiver Grassmannians. 相似文献
16.
本文应用陈怀惠和顾永兴关于Zalcman不正规性条件的改进结果,推广和加强了Lappan的一个正规定则.Lappan证明:若亚纯函数族中的所有函数的球面导数的幂方(大于2)在紧集上的积分一致有界,则该族是正则的.本文证明,把积分限制在函数值的模小于给定常数的子集上,结论仍然成立.同时,用高阶导数的积分替代球面导数的积分,得到十分一般的结果.另外对幂方为2的情形也进行了讨论. 相似文献
17.
Let β be a complex number,and a class of non-semisimple and non-solvable rank two Lie conformal algebras-(L)(β) are introduced.In this paper,conformal derivations,conformal quasiderivations,generalized conformal derivations and conformal biderivations of (L)(β) are studied.Besides,central extensions and conformal modules of rank one of (L)(β) are determined. 相似文献
18.
《代数通讯》2013,41(4):1643-1668
Abstract In this paper we construct two families of semisimple Hopf algebras of dimension 2 n+1, n ≥ 3. They are all constructed as Radford's biproducts. For these examples and their duals we compute their grouplike elements, centers, character algebras and Grothendieck rings. Comparing these facts we are able to show that depending on the dimension, representatives of one of the families are selfdual. We also prove that Hopf algebras from these families are neither triangular nor cotriangular and that their cocycle deformations are trivial. 相似文献
19.
Two Results on Metric Addition in Spherical Space 总被引:1,自引:0,他引:1
We establish the concept of metric addition in spherical space and obtain two related results. 相似文献