共查询到20条相似文献,搜索用时 0 毫秒
1.
许庆祥 《中国科学A辑(英文版)》2002,45(4):462-469
Diagonal invariant ideals of Toeplitz algebras defined on discrete groups are introduced and studied. In terms of isometric
representations of Toeplitz algebras associated with quasi-ordered groups, a character of a discrete group to be amenable
is clarified. It is proved that whenG is Abelian, a closed twosided non-trivial ideal of the Toeplitz algebra defined on a discrete Abelian ordered group is diagonal
invariant if and only if it is invariant in the sense of Adji and Murphy, thus a new proof of their result is given. 相似文献
2.
Let R be a Dubrovin valuation ring of a simple Artinian ring Q and let Q[X,] be the skew polynomial ring over Q in an indeterminate X, where is an automorphism of Q. Consider the natural map from Q[X,]XQ[X,] to Q, where Q[X,]XQ[X,] is the localization of Q[X,] at the maximal ideal XQ[X,] and set
, the complete inverse image of R by . It is shown that
is a Dubrovin valuation ring of Q(X,) (the quotient ring of Q[X,]) and it is characterized in terms of X and Q. In the case where R is an invariant valuation ring, the given automorphism is classified into five types, in order to study the structure of
(the value group of
). It is shown that there is a commutative valuation ring R with automorphism which belongs to each type and which makes
Abelian or non-Abelian. Furthermore, some examples are used to show that several ideal-theoretic properties of a Dubrovin valuation ring of Q with finite dimension over its center, do not necessarily hold in the case where Q is infinite-dimensional.
Presented by A. VerschorenMathematics Subject Classifications (2000) 16L99, 16S36, 16W60. 相似文献
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Diagonal Invariant Ideals of Topologically Graded C*-algebras 总被引:1,自引:0,他引:1
We study diagonal invariant ideals of topologically graded C~*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic. 相似文献
5.
In this paper, an extension of all Lie group actions on R
2to coordinates defined by potentials is given. This provides a new solution to the equivalence problems of curves under the projective group and two of its subgroups. The potentials correspond to integrals of higher and higher-order producing an infinite number of independent integral invariants. Applications to computer vision are discussed. 相似文献
6.
In this paper,we give transcendence bases of the rational invariants fields of the generalized classical groups and their subgroups B,N and T,and we also compute the orders of them.Furthermore,we give explicit generators for the rational invariants fields of the Borel subgroup and the Neron-Severi subgroup of the general linear group. 相似文献
7.
在不改变对角方阵各行、各列、主对角线、次对角线的元素之集的条件下,其变换群是n次对称群S_n的直积S_n×S_n的子群,因对角拉丁方、对角拉丁方正交侣、幻方、高次幻方、加乘幻方均属此类方阵,本文对构作这类对象及研究它们的计数有重要意义. 相似文献
8.
Martin Lorenz 《Algebras and Representation Theory》2001,4(3):293-304
Let G be a finite group acting by automorphism on a lattice A, and hence on the group algebra S=k[A]. The algebra of G-invariants in S is called an algebra of multiplicative invariants. We present an explicit version of a result of Farkas stating that multiplicative invariants of finite reflection groups are semigroup algebras. 相似文献
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10.
Let F q be a finite field of characteristic two, S be a nonsingular non-alternate symmetric matrix over F q and Ps n (F q , S) be the associated pseudo-symplectic group. Let Ps n (F q , S) act linearly on the polynomial ring F q [x 1,…, x n ]. In this note, we find an explicit set of generators of the ring of invariants of Ps n (F q , S) for n = 2, 4 and 2ν +1. In particular, the results assert that the ring of invariants of Ps 4(F q , S) is not a polynomial algebra but is an example of hypersurface and the ring of invariants of Ps 2ν+1(F q , S) is a complete intersection. 相似文献
11.
Jessica Hamm 《代数通讯》2013,41(8):3454-3484
We describe the multiplicative invariant algebras of the root lattices of all irreducible root systems under the action of the Weyl group. In each case, a finite system of fundamental invariants is determined and the class group of the invariant algebra is calculated. In some cases, a presentation and a Hironaka decomposition of the invariant algebra is given. 相似文献
12.
V. O. Manturov 《Acta Appl Math》2002,72(3):295-309
We propose a new method of generalizing classical link invariants for the case of virtual links. In particular, we have generalized the knot quandle, the knot fundamental group, the Alexander module, and the coloring invariants. The virtual Alexander module leads to a definition of VA-polynomial that has no analogue in the classical case (i.e. vanishes on classical links). 相似文献
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设F_q为有限域,f_i(x)=a_(i1)x_1~(d_(i1))+…+a_(in)x_n~(d_(in))+c_i(i=1,…,m)为F_q上一组对角多项式,用N(V)表示由f_i(i=1,…,m)确定的簇中的F_q.有理点的个数.通过应用Adolphson和Sperber所引进的牛顿多面体方法,证明了ord_qN(V)≥[1/d_1+…+1/d_n]-m,其中d_i=max{d_(1i),…,d_(mi)}.该结果在许多情形下可以改进Ax- Katz定理,并推广了Wan在m=1时得到的一个定理,而且我们对Wan的定理给出了一个不同的证明. 相似文献
15.
FU Zhi-guo 《东北数学》2006,(4)
Let ω be the element of maximal length in a finite irreducible Coxetersystem(W,S).In the present paper,we get the length of ω when(W,S)is of typeA_n B_n/C_n or D_n. 相似文献
16.
Let G be the finite cyclic group Z_2 and V be a vector space of dimension 2n with basis x_1,...,x_n,y_1,...,y_n over the field F with characteristic 2.If σ denotes a generator of G,we may assume that σ(x_i)= ayi,σ(y_i)= a~-1x_i,where a ∈ F.In this paper,we describe the explicit generator of the ring of modular vector invariants of F[V]~G.We prove that F[V]~G = F[l_i = x_i + ay_i,q_i = x_iy_i,1 ≤ i ≤ n,M_I = X_I + a~-I-Y_I],where I∈An = {1,2,...,n},2 ≤-I-≤ n. 相似文献
17.
For a faithful linear representation of a finite group G over a field of characteristic p, we study the ring of invariants. We especially study the polynomial and Cohen–Macaulay properties of the invariant ring. We first show that certain quotient rings of the invariant ring are polynomial rings by which we prove that the Hilbert ideal conjecture is true for a class of groups. In particular, we prove that the conjecture is true for vector invariant rings of Abelian reflection p-groups. Then we study the relationships between the invariant ring of G and that of a subgroup of G. Finally, we study the invariant rings of affine groups and show that, over a finite field, if an affine group contains all translations then the invariant ring is isomorphic to the invariant ring of a linear group. 相似文献
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从几何的角度给出了特征值不含1的二、三阶可逆矩阵可以相似对角化的一个充分条件和二、三阶可逆矩阵可以相似对角化的一个充分必要条件. 相似文献