共查询到20条相似文献,搜索用时 15 毫秒
1.
We give arguments for the necessity to employ quantum Clifford Hopf gebras in quantum field theory. The role of the antipode
is examined, Feynman diagrams are re-interpreted as tangles of graphical calculus. Regularization due to the design of convolution
Hopf gebras is given as a program for future research. 相似文献
2.
It is proved that the operator Lie algebra ε(T,T∗) generated by a bounded linear operator T on Hilbert space H is finite-dimensional if and only if T=N+Q, N is a normal operator, [N,Q]=0, and dimA(Q,Q∗)<+∞, where ε(T,T∗) denotes the smallest Lie algebra containing T,T∗, and A(Q,Q∗) denotes the associative subalgebra of B(H) generated by Q,Q∗. Moreover, we also give a sufficient and necessary condition for operators to generate finite-dimensional semi-simple Lie algebras. Finally, we prove that if ε(T,T∗) is an ad-compact E-solvable Lie algebra, then T is a normal operator. 相似文献
3.
Charles Buehrle 《Journal of Pure and Applied Algebra》2010,214(5):689-700
We use Kazhdan-Lusztig polynomials and subspaces of the polynomial ring C[x1,1,…,xn,n] to give a new construction of the Kazhdan-Lusztig representations of Sn. This construction produces exactly the same modules as those which Clausen constructed using a different basis in [M. Clausen, Multivariate polynomials, standard tableaux, and representations of symmetric groups, J. Symbolic Comput. (11), 5-6 (1991) 483-522. Invariant-theoretic algorithms in geometry (Minneapolis, MN, 1987)], and does not employ the Kazhdan-Lusztig preorders. We show that the two resulting matrix representations are related by a unitriangular transition matrix. This provides a C[x1,1,…,xn,n]-analog of results due to Garsia and McLarnan, and McDonough and Pallikaros, who related the Kazhdan-Lusztig representations to Young’s natural representations. 相似文献
4.
Tetiana Budnitska 《Linear algebra and its applications》2011,434(2):582-592
We study affine operators on a unitary or Euclidean space U up to topological conjugacy. An affine operator is a map f:U→U of the form f(x)=Ax+b, in which A:U→U is a linear operator and b∈U. Two affine operators f and g are said to be topologically conjugate if g=h-1fh for some homeomorphism h:U→U.If an affine operator f(x)=Ax+b has a fixed point, then f is topologically conjugate to its linear part A. The problem of classifying linear operators up to topological conjugacy was studied by Kuiper and Robbin [Topological classification of linear endomorphisms, Invent. Math. 19 (2) (1973) 83-106] and other authors.Let f:U→U be an affine operator without fixed point. We prove that f is topologically conjugate to an affine operator g:U→U such that U is an orthogonal direct sum of g-invariant subspaces V and W,
- •
- the restriction g∣V of g to V is an affine operator that in some orthonormal basis of V has the form(x1,x2,…,xn)?(x1+1,x2,…,xn-1,εxn) 相似文献
5.
Oleh Lopushansky 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(2):556-572
We investigate Hilbertian Hardy type spaces of complex analytic functions of infinite many variables, associated with compact unitary groups and the corresponding invariant Haar’s measures. For such analytic functions we establish a Cauchy type integral formula and describe natural domains. Also we show some relations between constructed spaces of analytic functions and the symmetric Fock space. 相似文献
6.
Alexandre Turull 《Archiv der Mathematik》2005,84(2):97-106
Let G be a finite group, N a normal subgroup of G, and an irreducible character of G. Clifford Theory studies a whole collection of related irreducible characters of all the subgroups of G that contain N. The relationships among these characters as well as their Schur indices are controlled by the Clifford class c Clif(G/N, F) of with respect to N over some field F. This is an equivalence class of central simple G/N-algebras. Assume now that G/N is cyclic. One can obtain a new isoclinic group
and character
by multiplying each element of each coset of N in G by an appropriate power of a fixed root of unity . We show that there is a simple formula to calculate the Clifford class
of
in terms of c and . Hence, the Clifford class c controls not only the Schur index of the characters of all the subgroups of G that contain N, it also controls the Schur indices of the characters of the corresponding characters of the isoclinic groups
When is a |G/N|-th root of 1, our formula shows that then
When = i and |G/N| = 2, the implicit transformation on Clif(Z/2Z, F) yields a group homomorphism of the group structure introduced on the Brauer-Wall group of F to describe the Schur indices of all the irreducible characters of the double covers of the symmetric and alternating groups.Received: 17 August 2001 相似文献
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9.
Yanan Lin 《Advances in Mathematics》2005,196(2):487-530
This article is to study relations between tubular algebras of Ringel and elliptic Lie algebras in the sense of Saito-Yoshii. Using the explicit structure of the derived categories of tubular algebras given by Happel-Ringel, we prove that the elliptic Lie algebra of type , , or is isomorphic to the Ringel-Hall Lie algebra of the root category of the tubular algebra with the same type. As a by-product of our proof, we obtain a Chevalley basis of the elliptic Lie algebra following indecomposable objects of the root category of the corresponding tubular algebra. This can be viewed as an analogue of the Frenkel-Malkin-Vybornov theorem in which they described a Chevalley basis for each untwisted affine Kac-Moody Lie algebra by using indecomposable representations of the corresponding affine quiver. 相似文献
10.
Dirk Hofmann 《Topology and its Applications》2006,153(15):2952-2961
11.
We formulate two open problems related to and, in a sense, suggested by the Reiterman-Tholen characterization of effective descent morphisms of topological spaces. 相似文献
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13.
We classify all (finitely dimensional) nilpotent Lie k-algebras h with 2-dimensional commutator ideals h′, extending a known result to the case where h′ is non-central and k is an arbitrary field. It turns out that, while the structure of h depends on the field k if h′ is central, it is independent of k if h′ is non-central and is uniquely determined by the dimension of h. In the case where k is algebraically or real closed, we also list all nilpotent Lie k-algebras h with 2-dimensional central commutator ideals h′ and dimkh?11. 相似文献
14.
Mitrofan M. Choban 《Topology and its Applications》2006,153(13):2320-2350
We consider completely regular Hausdorff spaces. In this paper we investigate the space of probability Radon measures P(X) on a space X and the property to be a Prohorov space. We prove that the space P(X) is sieve-complete if and only if X is sieve-complete. Every mapping generates the mapping . Some properties of the mapping P(φ) are studied. In particular, we investigate under which conditions the open continuous image of a Prohorov space is Prohorov. 相似文献
15.
A. Sevostyanov 《Selecta Mathematica, New Series》2002,8(4):637-703
We define deformations of W-algebras associated to comple semisimple Lie algebras by means of quantum Drinfeld-Sokolov reduction
procedure for affine quantum groups. We also introduce Wakimoto modules for arbitrary affine quantum groups and construct
free field resolutions and screening operators for the deformed W-algebras. We compare our results with earlier definitions
of q-W-algebras and of the deformed screening operators due to Awata, Kubo, Odake, Shiraishi [60],[6], [7], Feigin, E. Frenkel
[22] and E. Frenkel, Reshetikhin [34]. The screening operator and the free field resolution for the deformed W-algebra associated
to the simple Lie algebra sl2 coincide with those for the deformed Virasoro algebra introduced in [60].
The author is supported by the Swiss National Science Foundation. 相似文献
16.
Dirk Hofmann 《Topology and its Applications》2006,153(16):3180-3202
Motivated by the observation that both pretopologies and preapproach limits can be characterized as those convergence relations which have a unit for a suitable composition, we introduce the category Algu(T;V) of reflexive and unitary lax algebras, for a symmetric monoidal closed lattice V and a Set-monad T=(T,e,m). For T=U the ultrafilter monad, we characterize exponentiable morphisms in Algu(U;V). Further, we give a sufficient condition for an object to be exponentiable in the category Alg(U;V) of reflexive and transitive lax algebras. This specializes to known and new results for pretopological, preapproach and approach spaces. 相似文献
17.
Y. Kosmann-Schwarzbach 《Acta Appl Math》1995,41(1-3):153-165
We show that to any Poisson manifold and, more generally, to any triangular Lie bialgebroid in the sense of Mackenzie and Xu, there correspond two differential Gerstenhaber algebras in duality, one of which is canonically equipped with an operator generating the graded Lie algebra bracket, i.e. with the structure of a Batalin-Vilkovisky algebra. 相似文献
18.
Grega Cigler 《Linear algebra and its applications》2011,435(6):1285-1295
Let G and H be groups of complex n×n matrices. We say that G is an H-like group if every matrix in G is similar to a matrix from H. For several groups H we consider two questions:
- (A)
- Is every H-like group (simultaneously) similar to a subgroup of H?
- (B)
- Is H the only H-like group containing H? Among other results we prove that the symmetric group Sn is the only Sn-like group containing Sn.
19.
M.A. Rodr?´guez-Andrade G. Aragón-González 《Linear algebra and its applications》2011,434(5):1238-1254
We present an algorithmic proof of the theorem on generalized real scalar product spaces with arbitrary signature. We use Clifford algebras to compute the factorization of a given transformation as a product of reflections with respect to hyperplanes. The relationship with the Cartan-Dieudonné-Scherk theorem is also discussed in relation to the minimum number of reflections required to decompose a given orthogonal transformation. 相似文献
20.
Abdukadir Obul 《Journal of Pure and Applied Algebra》2007,208(2):445-448
It is known from [M. Auslander, M.I. Platzeck, I. Reiten, Coxeter functors without diagrams, Trans. Amer. Math. Soc. 250 (1979) 1-46] and [C.M. Ringel, PBW-basis of quantum groups, J. Reine Angew. Math. 470 (1996) 51-85] that the Bernstein-Gelfand-Ponomarev reflection functors are special cases of tilting functors and these reflection functors induce isomorphisms between certain subalgebras of Ringel-Hall algebras. In [A. Wufu, Tilting functors and Ringel-Hall algebras, Comm. Algebra 33 (1) (2005) 343-348] the result from [C.M. Ringel, PBW-basis of quantum groups, J. Reine Angew. Math. 470 (1996) 51-85] is generalized to the tilting module case by giving an isomorphism between two Ringel-Hall subalgebras. In [J. Miyashita, Tilting Modules of Finite Projective Dimension, Math. Z. 193 (1986) 113-146] Miyashita generalized the tilting theory by introducing the tilting modules of finite projective dimension. In this paper the result in [A. Wufu, Tilting functors and Ringel-Hall algebras, Comm. Algebra 33 (1) (2005) 343-348] is generalized to the tilting modules of finite projective dimension. 相似文献