共查询到20条相似文献,搜索用时 31 毫秒
1.
Piotr M. Hajac Rainer Matthes Wojciech Szymanski 《Algebras and Representation Theory》2006,9(2):121-146
The irreducible *-representations of the polynomial algebra
of the quantum3-sphere introduced by Calow and Matthes are classified. The K-groups of its universal C*-algebra are shown to coincide with their classical counterparts. The U(1)-action on
corresponding for p=1=q to the classical Hopf fibration is proven to be Galois (free). The thus obtained locally trivial Hopf–Galois extension is
shown to be equivariantly projective (admitting a strong connection) and non-cleft. The latter is proven by determining an
appropriate pairing of cyclic cohomology and K-theory.
Presented by S. L. Woronowicz
Mathematics Subject Classifications (2000) 16W30, 46L87. 相似文献
2.
Josefina Alvarez Magali Folch-Gabayet Salvador Pérez-Esteva 《Journal of Fourier Analysis and Applications》2001,7(1):49-62
The purpose of this article is to study the Hilbert space W2\mathcal{ W}^2 consisting of all solutions of the Helmholtz equation Du+u=0\Delta u+u=0 in
\BbbR2\Bbb{R}^2 that are the image under the Fourier transform of L2L^2 densities in the unit circle. We characterize this space as a close subspace of the Hilbert space H2\mathcal{ H}^2 of all functions belonging to L2( | x | -3dx) L^2( | x | ^{-3}dx) jointly with their angular and radial derivatives, in the complement of the unit disk in
\BbbR2\Bbb{R}^2. We calculate the reproducing kernel of W2\mathcal{ W}^2 and study its reproducing properties in the corresponding spaces Hp\mathcal{H}^p, for $p>1$p>1. 相似文献
3.
For an algebra
with an action of a Hopf algebra
we establish the pairing between equivariant cyclic cohomology and equivariant K-theory for
. We then extend this formalism to compact quantum group actions and show that equivariant cyclic cohomology is a target space
for the equivariant Chern character of equivariant summable Fredholm modules. We prove an analogue of Julg's theorem relating
equivariant K-theory to ordinary K-theory of the C*-algebra crossed product, and characterize equivariant vector bundles on quantum homogeneous spaces. 相似文献
4.
Farkhad Nematjonovich Arzikulov Shavkat Abdullayevich Ayupov 《Algebras and Representation Theory》2013,16(1):289-301
In the given article, enveloping C*-algebras of AJW-algebras are considered. Conditions are given, when the enveloping C*-algebra of an AJW-algebra is an AW*-algebra, and corresponding theorems are proved. In particular, we proved that if $\mathcal{A}$ is a real AW*-algebra, $\mathcal{A}_{sa}$ is the JC-algebra of all self-adjoint elements of $\mathcal{A}$ , $\mathcal{A}+i\mathcal{A}$ is an AW*-algebra and $\mathcal{A}\cap i\mathcal{A} = \{0\}$ then the enveloping C*-algebra $C^*(\mathcal{A}_{sa})$ of the JC-algebra $\mathcal{A}_{sa}$ is an AW*-algebra. Moreover, if $\mathcal{A}+i\mathcal{A}$ does not have nonzero direct summands of type I2, then $C^*(\mathcal{A}_{sa})$ coincides with the algebra $\mathcal{A}+i\mathcal{A}$ , i.e. $C^*(\mathcal{A}_{sa})= \mathcal{A}+i\mathcal{A}$ . 相似文献
5.
Andrew R. Linshaw 《Transformation Groups》2010,15(2):427-448
Given a simple vertex algebra A \mathcal{A} and a reductive group G of automorphisms of A \mathcal{A} , the invariant subalgebra AG {\mathcal{A}^G} is strongly finitely generated in most examples where its structure is known. This phenomenon is subtle, and is generally
not true of the classical limit of AG {\mathcal{A}^G} , which often requires infinitely many generators and infinitely many relations to describe. Using tools from classical invariant
theory, together with recent results on the structure of the W1 + ¥ {\mathcal{W}_{{1 + }\infty }} algebra, we establish the strong finite generation of a large family of invariant subalgebras of βγ-systems, bc-systems, and bcβγ-systems. 相似文献
6.
For a finite triangulation of the plane with faces properly coloured white and black, let
AW\mathcal{A}_{W}
be the abelian group constructed by labelling the vertices with commuting indeterminates and adding relations which say that
the labels around each white triangle add to the identity. We show that
AW\mathcal{A}_{W}
has free rank exactly two. Let
AW*\mathcal{A}_{W}^{*}
be the torsion subgroup of
AW\mathcal{A}_{W}
, and
AB*\mathcal{A}_{B}^{*}
the corresponding group for the black triangles. We show that
AW*\mathcal{A}_{W}^{*}
and
AB*\mathcal{A}_{B}^{*}
have the same order, and conjecture that they are isomorphic.
For each spherical latin trade W, we show there is a unique disjoint mate B such that (W,B) is a connected and separated bitrade. The bitrade (W,B) is associated with a two-colourable planar triangulation and we show that W can be embedded in
AW*\mathcal{A}_{W}^{*}
, thereby proving a conjecture due to Cavenagh and Drápal. The proof involves constructing a (0,1) presentation matrix whose
permanent and determinant agree up to sign. The Smith normal form of this matrix determines
AW*\mathcal{A}_{W}^{*}
, so there is an efficient algorithm to construct the embedding. Contrasting with the spherical case, for each genus g≥1 we construct a latin trade which is not embeddable in any group and another that is embeddable in a cyclic group. 相似文献
7.
Eric Sommers 《Transformation Groups》2011,16(3):889-911
Let H*( Be ) {H^*}\left( {{\mathcal{B}_e}} \right) be the total Springer representation of W for the nilpotent element e in a simple Lie algebra
\mathfrakg \mathfrak{g} . Let Λ
i
V denote the ith exterior power of the reflection representation V of W. The focus of this paper is on the algebra of W-invariants in
H*( Be ) ?L*V {H^*}\left( {{\mathcal{B}_e}} \right) \otimes {\Lambda^*}V 相似文献
8.
Lutz Strüngmann 《Israel Journal of Mathematics》2006,151(1):29-51
LetR be a unital associative ring and
two classes of leftR-modules. In [St3] the notion of a (
) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses
is called a (
) pair if it is maximal with respect to the classes
and the condition Ext
R
1
(V, W)=0 for all
. In this paper we study
pairs whereR = ℤ and
is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every
pair is singly cognerated underV=L.
The author was supported by a DFG grant. 相似文献
9.
Huffman, Park and Skoug established several results involving Fourier-Feynman transform and convolution for functionals in
a Banach algebra S on the classical Wiener space. Chang, Kim and Yoo extended these results to abstract Wiener space for a more generalized
Fresnel class $
\mathcal{F}_{\mathcal{A}_1 ,\mathcal{A}_2 }
$
\mathcal{F}_{\mathcal{A}_1 ,\mathcal{A}_2 }
A1,A2 than the Fresnel class $
\mathcal{F}
$
\mathcal{F}
(B)which corresponds to the Banach algebra S. In this paper we study Fourier-Feynman transform, convolution and first variation of unbounded functionals on abstract Wiener
space having the form
|