Gaussian Cubature Arising from Hybrid Characters of Simple Lie Groups

Lie groups with two different root lengths allow two ‘mixed sign’ homomorphisms on their corresponding Weyl groups, which in turn give rise to two families of hybrid Weyl group orbit functions and characters. In this paper we extend the ideas leading to the Gaussian cubature formulas for families of polynomials arising from the characters of irreducible representations of any simple Lie group, to new cubature formulas based on the corresponding hybrid characters. These formulas are new forms of Gaussian cubature in the short root length case and new forms of Radau cubature in the long root case. The nodes for the cubature arise quite naturally from the (computationally efficient) elements of finite order of the Lie group.     

Algebra homomorphisms defined via convoluted semigroups and cosine functions

Transform methods are used to establish algebra homomorphisms related to convoluted semigroups and convoluted cosine functions. Such families are now basic in the study of the abstract Cauchy problem. The framework they provide is flexible enough to encompass most of the concepts used up to now to treat Cauchy problems of the first- and second-order in general Banach spaces. Starting with the study of the classical Laplace convolution and a cosine convolution, along with associated dual transforms, natural algebra homomorphisms are introduced which capture the convoluted semigroup and cosine function properties. These correspond to extensions of the Cauchy functional equation for semigroups and the abstract d'Alembert equation for the case of cosine operator functions. The algebra homomorphisms obtained provide a way to prove Hille-Yosida type generation theorems for the operator families under consideration.     

r模同态的{1}-逆与{2}-逆

本文探讨模同态广义逆在环模理论中的应用．利用模同态的{1}-逆与{2}-逆，分别给出了一类环及一类重要模的特征刻画．     

Row and Column Removal Theorems for Homomorphisms of Specht Modules and Weyl Modules

We prove a q-analogue of the row and column removal theorems for homomorphisms between Specht modules proved by Fayers and the first author [16]. These results can be considered as complements to James and Donkin’s row and column removal theorems for decomposition numbers of the symmetric and general linear groups. In this paper we consider homomorphisms between the Specht modules of the Hecke algebras of type A and between the Weyl modules of the q-Schur algebra.This research was supported by ARC grant DP0343023. The first author was also supported by a Sesqui Research Fellowship at the University of Sydney.     

Quasi-triangular Hopf algebras and invariant Jacobians

We show that two module homomorphisms for groups and Lie algebras established by Xi can be generalized to the setting of quasi-triangular Hopf algebras. These module homomorphisms played a key role in his proof of a conjecture of Yau (1998). They will also be useful in the problem of decomposition of tensor products of modules. Additionally, we give another generalization of result of Xi in terms of Chevalley-Eilenberg complex.     

Study of the Modules over Rings and Their Extensions

Ukrainian Mathematical Journal - We study the problem of transfer of the properties of some types of modules under identity preserving ring homomorphisms. These studies seem to be overlooked in the...     

L-fuzzy子环的L-fuzzy模的L-fuzzy同态

给出一种真正的 L- fuzzy子环的 L- fuzzy同态和 L- fuzzy同构等概念 ,证明 L- fuzzy模在 L- fuzzy同态映射下不变     

Noncommutative symmetric functions and an amazing matrix

We present a simple way to derive the results of Diaconis and Fulman [P. Diaconis, J. Fulman, Foulkes characters, Eulerian idempotents, and an amazing matrix, arXiv:1102.5159] in terms of noncommutative symmetric functions.     

Noetherian Pi-Rings

Rings are associative and have a unit and subrings are assumed to have the same unit. Ring homomorphisms are unitary, as are modules. Ideal means two-sided ideal.     

Differential projective modules over differential rings

Differential modules over a commutative differential ring which are projective as ring modules, with differential homomorphisms, form an additive category. Every projective ring module is shown occurs as the underlying module of a differential module. Differential modules, projective as ring modules, are shown to be direct summands of differential modules free as ring modules; those which are differential direct summands of differential direct sums of the ring being induced from the subring of constants. Every differential module finitely generated and projective as a ring module is shown to have this form after a faithfully flat finitely presented differential extension of the base.     

T-Radicals and E-Radicals in the Category of Modules

We introduce two classes of radicals by means of tensor product of modules and module homomorphisms and prove some properties of these radicals and their connection with attracting modules.     

Topological modules of continuous homomorphisms

In this paper, we consider the notion of module homomorphisms in the general topological module setting and establish their linearity and continuity under some suitable conditions. We also introduce the strict and uniform topologies on the modules of continuous linear homomorphisms and study their various properties.     

Logarithmic intertwining operators and associative algebras

We establish an isomorphism between the space of logarithmic intertwining operators among suitable generalized modules for a vertex operator algebra and the space of homomorphisms between suitable modules for a generalization of Zhu’s algebra given by Dong-Li-Mason.     

Local to global equivalence for homomorphisms

his paper studies the connection between sheaf cohomology and local vs. global equivalence for homomorphisms of finitely presented modules over commutative rings. The connection between cohomology and the local/global problem is worked out, basic cohomology sequences are derived and connections with the known interpretation of local/global equivalence in terms of modules and some calculations are given.     

Some Weyl modules and cohomology for algebraic groups

Abstract

In this article, we give a generalization of O’Halloran’s theorem that gives rise to families of Weyl modules with simple radicals. This generalization is then applied to simply connected, semisimple algebraic groups of types B, C, and D. We also construct families of Weyl modules with formal characters of length 4, and compute the extensions and cohomology of simple modules associated with these Weyl modules.     

ON WEYL MODULES OVER AFFINE LIE ALGEBRAS IN PRIME CHARACTERISTIC

We construct a family of homomorphisms between Weyl modules for affine Lie algebras in characteristic p, which supports our conjecture on the strong linkage principle in this context. We also exhibit a large class of reducible Weyl modules beyond level one, for p not necessarily small.     

Lower complete intersection dimension over local homomorphisms

We introduce and study a theory of lower complete intersection dimension over local homomorphisms which encompasses the theory of lower complete intersection dimension for finite modules over local rings introduced by Gerko. In particular, we show that the lower complete intersection dimension over local homomorphisms reflects the complete intersection property of base rings as expected. As an application, we prove that the converse of a theorem of Sather-Wagstaff is also true.     

量子环面C-1上的一族Noether模

记C_-1为q=-1 的量子环面Lie代数. 本文以Laurent 多项式环C[x^±1] 为表示空间, 构造了C_-1上的一类Noether 但非Artin 的模, 并确定了它们的全部子模和商模以及它们之间的全体模同态,最后指出该模与A₁型loop代数忠实表示的关系.     

关于L内射覆盖

We use the class of L-injective modules to define L-injective covers, and provide the characterizations of L-injective covers by the properties of kernels of homomorphisms. We prove that the right L-noetherian right L-hereditary ring is just such that every right R-module has an L-injective cover which is monic. We also use kernels of homomorphisms to investigate L-simple L-injective covers and give some constructions of L-simple L-injective covers.