共查询到20条相似文献,搜索用时 15 毫秒
1.
Doug Bullock Jó zef H. Przytycki 《Proceedings of the American Mathematical Society》2000,128(3):923-931
We describe, for a few small examples, the Kauffman bracket skein algebra of a surface crossed with an interval. If the surface is a punctured torus the result is a quantization of the symmetric algebra in three variables (and an algebra closely related to a cyclic quantization of )). For a torus without boundary we obtain a quantization of ``the symmetric homologies" of a torus (equivalently, the coordinate ring of the -character variety of ). Presentations are also given for the four-punctured sphere and twice-punctured torus. We conclude with an investigation of central elements and zero divisors.
2.
Doug Bullock 《Proceedings of the American Mathematical Society》1997,125(6):1835-1839
We introduce a new technique for estimating the number of generators of the Kauffman bracket skein module of a three manifold; one which requires the construction of linear functionals on a simpler version of the module. Of particular interest is the use of representations of the fundamental group into to generate the functionals.
3.
Bo Lu 《数学研究通讯:英文版》2013,29(1):41-50
Let $R$ be a ring, and let $(\mathcal{F}, C)$ be a cotorsion theory. In this article, the
notion of $\mathcal{F}$-perfect rings is introduced as a nontrial generalization of perfect rings
and A-perfect rings. A ring $R$ is said to be right $\mathcal{F}$-perfect if $F$ is projective relative
to $R$ for any $F ∈ \mathcal{F}$. We give some characterizations of $\mathcal{F}$-perfect rings. For example,
we show that a ring $R$ is right $\mathcal{F}$-perfect if and only if $\mathcal{F}$-covers of finitely generated
modules are projective. Moreover, we define $\mathcal{F}$-perfect modules and investigate some
properties of them. 相似文献
4.
V. Guirardel 《Commentarii Mathematici Helvetici》1998,73(1):89-121
This article shows how to approximate a stable action of a finitely presented group on an -tree by a simplicial one while keeping control over arc stabilizers. For instance, every small action of a hyperbolic group on an -tree can be approximated by a small action of the same group on a simplicial tree. The techniques we use highly rely on Rips's study of stable actions on -trees and on the dynamical study of exotic components by D. Gaboriau.
Received: 22 October, 1997 相似文献
5.
A New Proof of Diophantine Equation $\Bigg( \begin{matrix} n \\ 2 \end{matrix} \Bigg) = \Bigg( \begin{matrix} m \\ 4 \end{matrix} \Bigg)$
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Huilin Zhu 《数学研究通讯:英文版》2009,25(3):282-288
By using algebraic number theory and $p$-adic analysis method, we give a new and simple proof of Diophantine equation $\Bigg( \begin{matrix} n \\ 2 \end{matrix} \Bigg) =\Bigg( \begin{matrix} m \\ 4 \end{matrix} \Bigg)$. 相似文献
6.
Don Monk 《Algebra Universalis》2002,47(4):495-500
For any Boolean algebra A, is the smallest cardinality of an infinite partition of unity in A. A tower in a Boolean algebra A is a subset X of A well-ordered by the Boolean ordering, with but with is the smallest cardinality of a tower of A. Given a linearly ordered set L with first element, the interval algebra of L is the algebra of subsets of L generated by the half-open intervals [a, b). We prove that there is an atomless interval algebra A such that .
Received January 21, 2002; accepted in final form March 13, 2002. 相似文献
7.
Pulling back the weight system associated with the exceptional Lie algebra by a modification of the universal Vassiliev-Kontsevich invariant yields a link invariant; extending it to 3-nets, we derive a recursive algorithm for its evaluation. Received: April 16, 1998 相似文献
8.
In this paper, the irreducible p, q‐representations of the Lie algebras $\mathcal {G}(0,1)$ and $\mathcal {G}(0,0)$ are discussed. We prove two theorems that classify certain irreducible p, q‐representations of these Lie algebras and construct their one variable models in terms of p, q‐derivative and dilation operators. As an application, we derive a p, q‐special function identity based on one such model. 相似文献
9.
Christopher Manon 《Transformation Groups》2013,18(4):1165-1187
We construct and study a family of toric degenerations of the Cox ring of the moduli of quasi-parabolic principal SL3( $ \mathbb{C} $ ) bundles on a smooth, marked curve (C, $ \vec{p} $ ): Elements of this algebra have a well known interpretation as conformal blocks, from the Wess-Zumino-Witten model of conformal field theory. For the genus 0; 1 cases we find the level of conformal blocks necessary to generate the algebra. In the genus 0 case we also find bounds on the degrees of relations required to present the algebra. As a consequence we obtain a toric degeneration for the projective coordinate ring of an effective divisor on the moduli $ {{\mathcal{M}}_{{C,\vec{p}}}}\left( {\mathrm{S}{{\mathrm{L}}_3}\left( \mathbb{C} \right)} \right) $ of quasi-parabolic principal SL3( $ \mathbb{C} $ ) bundles on (C, $ \vec{p} $ ). Along the way we recover positive polyhedral rules for counting conformal blocks. 相似文献
10.
WeiPingLi 《数学学报(英文版)》2003,19(2):233-244
In this paper,we count the number of SL2(F2^s)-representations of torus knot groups up to a conjugacy.For the finite field F2^s with character 2,the counting method is similar to that in out previous work[1].Explicit formulae of the effective counting are given in this paper.Twisted Alexander polynomials related to those reprsentations are discussed. 相似文献
11.
Jian Hua Chen 《数学学报(英文版)》2002,18(4):765-778
In this paper, we apply the soliton theory to the case of isometric immersion in differential geometry and obtain a family
of isometric immersions from M
n
1(c
1) ×M
n
2(c
2) to space forms M
n
(c) by introducing 2-parameter loop algebra.
Received July 14, 1999, Accepted June 15, 2000 相似文献
12.
S. Racanière 《Commentarii Mathematici Helvetici》2003,78(2):394-417
The quasi-Hamiltonian reduction of at a regular value, in the centre of SU(n), of the moment map is isomorphic to a moduli-space of semi-stable vector bundles over a Riemann surface. We describe the
restriction map from the equivariant cohomology of to the cohomology of the moduli space in terms of natural multiplicative generators of these cohomologies.
Received: May 28, 2002 相似文献
13.
Guo-lian~Xu ChandrajitL.Bajaj 《计算数学(英文版)》2003,21(5):681-688
In this paper, we provide simple and explicit formulas for computing Riemannian curvatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in IR^k with k ≥ 3. 相似文献
14.
由$\widehat{psl(2|2)^{(2)}}_{k}$非线性$\sigma$ -模型加上WZ -项得到的WZW模型是共形场论,它具有李超代数$psl(2|2)$对称性.该文用向量相干态方法给出了李超代数$psl(2|2)$的微分算子表示.并在此基础上给出了扭曲Kac-Moody李超代数 $\widehat{psl(2|2)^{(2)}}_{k}$自由场实现,相应共形场论的中心荷为$-2$. 相似文献
15.
设$p>0$, $\mu$和$\mu_{1}$是$[0,1)$上的正规函数. 本文首先给出了$\mathbb{C}^{n}$中单位球上$\mu$-Bergman空间$A^{p}(\mu)$的几种等价刻画;
然后
分别刻画了$A^{p}(\mu)$到$A^{p}(\mu_{1})$的
微分复合算子$D_{\varphi}$为有界算子以及紧算子的充要条件, 同时给出了当$p>1$时$D_{\varphi}$为
$A^{p}(\mu)$到$A^{p}(\mu_{1})$上紧算子的一种简捷充分条件和必要条件. 相似文献
16.
Kyriakos Keremedis 《Mathematical Logic Quarterly》2012,58(3):130-138
Given a set X, $\mathsf {AC}^{\mathrm{fin}(X)}$ denotes the statement: “$[X]^{<\omega }\backslash \lbrace \varnothing \rbrace$ has a choice set” and $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )$ denotes the family of all closed subsets of the topological space $\mathbf {2}^{X}$ whose definition depends on a finite subset of X. We study the interrelations between the statements $\mathsf {AC}^{\mathrm{fin}(X)},$ $\mathsf {AC}^{\mathrm{fin}([X]^{<\omega })},$ $\mathsf {AC}^{\mathrm{fin} (F_{n}(X,2))},$ $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$ and “$\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$has a choice set”. We show:
- (i) $\mathsf {AC}^{\mathrm{fin}(X)}$ iff $\mathsf {AC}^{\mathrm{fin}([X]^{<\omega } )}$ iff $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set iff $\mathsf {AC}^{\mathrm{fin}(F_{n}(X,2))}$.
- (ii) $\mathsf {AC}_{\mathrm{fin}}$ ($\mathsf {AC}$ restricted to families of finite sets) iff for every set X, $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set.
- (iii) $\mathsf {AC}_{\mathrm{fin}}$ does not imply “$\mathcal {K}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set($\mathcal {K}(\mathbf {X})$ is the family of all closed subsets of the space $\mathbf {X}$)
- (iv) $\mathcal {K}(\mathbf {2}^{X})\backslash \lbrace \varnothing \rbrace$ implies $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$ but $\mathsf {AC}^{\mathrm{fin}(X)}$ does not imply $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$.
17.
S. V. Kerov 《Journal of Mathematical Sciences》1992,59(5):1072-1078
Methods previously suggested by A. M. Vershik and the author are used to calculate the traces and group of dimensions for the subalgebra of Sp (2m)-invariant in \(\mathop \otimes \limits^\infty M_{2m} \mathbb{C}\) 相似文献
18.
The $\mathbb{Z}_{+}$-ring is an important invariant in the theory of tensor category. In this paper, by using matrix method, we describe all irreducible $\mathbb{Z}_{+}$-modules over a $\mathbb{Z}_{+}$-ring $\mathcal{A}$, where $\mathcal{A}$ is a commutative ring with a $\mathbb{Z}_{+}$-basis{$1$, $x$, $y$, $xy$} and relations: $$ x^{2}=1,\;\;\;\;\; y^{2}=1+x+xy.$$We prove that when the rank of $\mathbb{Z}_{+}$-module $n\geq5$, there does not exist irreducible $\mathbb{Z}_{+}$-modules and when the rank $n\leq4$, there exists finite inequivalent irreducible $\mathbb{Z}_{+}$-modules, the number of which is respectively 1, 3, 3, 2 when the rank runs from 1 to 4. 相似文献
19.
A maximum (v, G, λ)-PD and a minimum (v, G, λ)-CD axe studied for 2 graphs of 6 vertices and 7 edges. By means of "difference method" and "holey graph design", we obtain the result: there exists a (v, Gi, λ)-OPD (OCD) for v ≡ 2, 3, 4, 5, 6 (mod 7), λ ≥ 1, i = 1, 2. 相似文献