共查询到20条相似文献,搜索用时 31 毫秒
1.
V. N. Tolstoy 《Czechoslovak Journal of Physics》2001,51(12):1453-1458
Tensor operators are discussed for Hopf algebras and, in particular, for a quantum (q-deformed) algebraUq(g), whereg is any simple finite-dimensional or affine Lie algebra. These operators are defined via an adjoint action in a Hopf algebra.
There are two types of the tensor operators which correspond to two coproducts in the Hopf algebra. In the case of tensor
products of two tensor operators one can obtain 8 types of the tensor operators and so on. We prove the relations which can
be a basis for a proof of the Wigner-Eckart theorem for the Hopf algebras. It is also shown that in the case ofUq(g) a scalar operator can be differed from an invariant operator but atq=1 these operators coincide.
Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June
2001.
Supported by Russian Foundation for Fundamental Research, grant 99-01-01163, and by INTAS-00-00055. 相似文献
2.
J. C. Pérez Bueno 《Czechoslovak Journal of Physics》1997,47(12):1275-1282
It is shown that all members in the family of deformed Hopf algebras corresponding to the graded contractions of the inhomogeneous
algebrasiso(p,q),p +q=N, have a bicrossproduct structure.
Presented at the 6th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 19–21 June
1997.
This research has been partially supported by a research grant from the Spanish CICYT. 相似文献
3.
Generalization of Hopf algebraslq (2) by weakening the invertibility of the generatorK, i.e., exchanging its invertibilityKK
−1=1 to the regularity K
K=K is studied. Two weak Hopf algebras are introduced: a weak Hopf algebrawslq (2) and aJ-weak Hopf algebravslq (2) which are investigated in detail. The monoids of group-like elements ofwslq (2) andvslq (2) are regular monoids, which supports the general conjucture on the connection betweek weak Hopf algebras and regular monoids.
A quasi-braided weak Hopf algebraŪqw is constructed fromwslq (2). It is shown that the corresponding quasi-R-matrix is regular Rw
wRw=Rw.
Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June
2001
Project (No. 19971074) supported by the National Natural Science Foundation of China. 相似文献
4.
Marc de Montigny 《Czechoslovak Journal of Physics》2000,50(11):1297-1302
I explain how the concept ofgrading of Lie algebras can be used to investigate the appearance of central charges during a contraction. I illustrate the method
with the kine-matical algebras of spacetime.
Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. 相似文献
5.
We introduce two types of algebras which include respectively the well known reflection equation (RE) and Faddeev-Reshetikhin-Takhtayan
algebras associated with a quasitriangular Hopf algebraH. We show that these two types of algebras are twist-equivalent. It follows that a RE algebra is a module algebra over a twisted
tensor square ofH. We present some applications to the equivariant quantization.
Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002. 相似文献
6.
V. D. Lyakhovsky 《Czechoslovak Journal of Physics》1996,46(2-3):227-234
Quantum duality principle is applied to a study of classical limits of quantum algebras and groups. For a certain type of Hopf algebras the explicit procedure to construct both classical limits is presented. The canonical forms of quantized Lie-bialgebras are proved to be two-parametric varieties with two classical limits called dual. When considered from the point of view of quantized symmetries, such varieties can have boundaries that are noncommutative and noncocommutative. In this case the quantum duality and dual limits still exist while instead of Lie bialgebra one has a pair of tangent vector fields.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.I am heartily grateful to Prof. J. Lukierski for fruitful discussions and to all the scientists of the Institute of Theoretical Physics of Wroclaw University for their warm hospitality.The work is supported in part by the International Sci. Foundation, Grant N U9J000, and by the Russian Foundation for Fundamental Research, Grant No 95-01-00569a. 相似文献
7.
Bertfried Fauser 《Czechoslovak Journal of Physics》2000,50(11):1221-1228
In a recent work we have shown that quantum Clifford algebras — i.e. Clifford algebras of an arbitrary bilinear form — are
closely related to the deformed structures asq-spin groups, Hecke algebras,q-Young operators and deformed tensor products. The question to relate Manin’s approach to quantum Clifford algebras is addressed
here. Explicit computations using the CLIFFORD Maple package are exhibited. The meaning of non-commutative geometry is reexamined
and interpreted in Clifford algebraic terms.
Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. 相似文献
8.
A. Horzela 《Czechoslovak Journal of Physics》2000,50(11):1245-1250
The Wigner problem,i.e. the search for quantum mechanical commutation relations consistent with the Heisenberg evolution equations of a given form
is studied. In the framework of recently proposed generalization of the Wigner approach the classical analogy is postulated
for the form of the time evolution equations only and the forms of the time evolution and symmetry generators are nota priori assumed. Instead of that the set of basic, physically justified algebraic relations is required to have a Lie algebra structure.
Here the problem is formulated for the system of two particles interacting harmonically and a noncanonical Lie algebra of
fundamental quantum mechanical quantities, alternative to the standard canonical one, is found. The solution of the nonrelativistic
problem suggests what kind of algebras could be investigated as its relativistic analogues.
Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. 相似文献
9.
T. Skrypnyk 《Czechoslovak Journal of Physics》2002,52(11):1283-1288
We construct a family of infinite-dimensional quasigraded Lie algebras, that could be viewed as deformation of the graded
loop algebras. Using them we obtain new series of integrable Hamiltonian systems on semisimple Lie algebras and their extensions.
Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002. 相似文献
10.
This paper is concerned with a new class of graded algebras naturally uniting within a single framework various deformations
of the Witt, Virasoro and other Lie algebras based on twisted and deformed derivations, as well as color Lie algebras and
Lie superalgebras.
Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.
Supported by the Liegrits network
Supported by the Crafoord foundation 相似文献
11.
André Lichnerowicz 《Letters in Mathematical Physics》1979,3(6):495-502
The twisted products play an important role in Quantum Mechanics [1, 2]. We introduce here a distinction between Vey *ν-products and strong Vey *ν-products and prove that each *ν-product is equivalent to a Vey *ν-product. If b
3(W)=0, the symplectic manifold (W, F) admits strong Vey *ν-products. If b
2(W)=0, all *ν-products are equivalent as well as the Vey Lie algebras. In the general case, we characterize the formal Lie algebras which
are generated by a *ν-product and we prove that the existence of a *ν-product is equivalent to the existence of a formal Lie algebra infinitesimally equivalent to a Vey Lie algebra at the first
order. 相似文献
12.
A systematic method to constructN-body integrable systems is introduced by means of phase space realizations of universal enveloping Hopf algebras. A particular realization for theso(2, 1) case (Gaudin system) is analysed and an integrable quantum deformation is constructed by using quantum algebras as Poisson-Hopf symmetries.Presented at the 5th International Colloquium on Quantum Groups: Quantum Groups and Integrable Systems, Prague, 20–22 June 1996. 相似文献
13.
Multiparametric quantum gl(2) algebras are presented according to a classification based on their corresponding Lie bialgebra structures. From them, the non-relativistic limit leading to quantum harmonic oscillator algebras is implemented in the form of generalized Lie bialgebra contractions. 相似文献
14.
Hans Tilgner 《International Journal of Theoretical Physics》1973,7(1):67-75
The symplectic vector spaceE of theq andp's of classical mechanics allows a basis free definition of the Poisson bracket in the symmetric algebra overE. Thus the symmetric algebra overE becomes a Lie algebra, which can be compared with the quantum mechanical Weyl algebra with its commutator Lie structure.
The universality of the Weyl algebra is used to study the well-known ‘classical’ Moyal realisation of the Weyl algebra in
the symmetric algebra. Quantisations are defined as linear mappings of the underlying vector spaces of the two algebras. It
is shown that the classical Lie algebra is −2 graded, whereas the quantum Lie algebra is not. This proves that they are not
isomorphic, and hence there is no Dirac quantisation. 相似文献
15.
A. Zuevsky 《Czechoslovak Journal of Physics》2005,55(11):1545-1551
We introduce bicomplex structures associated with Saveliev-Vershik continual Lie algebras, and derive non-linear dynamical
systems resulting from the bicomplex conditions. Examples related to classes of continual Lie algebras, including contact
Lie, Poisson bracket, and Hilbert-Cartan ones are discussed. Using the bicomplex linearization problem, we derive corresponding
conservation laws.
Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005. 相似文献
16.
A general way for constructing square lattice systems with certain Lie algebraic or quantum Lie algebraic symmetries is presented.
These models give rise to series of integrable (stochastic) systems. As examples theAn-symmetric chain models and theSU(2)-invariant ladder models are investigated.
Presented at the 10th Colloquium on Quantum Groups: “Quantum Groups and Intergrable Systems”, Prague, 21–23 June, 2001
SFB 256; BiBoS; CERFIM(Locarno); Acc. Arch.; USI(Mendriso) 相似文献
17.
Olga Kravchenko 《Letters in Mathematical Physics》2007,81(1):19-40
Structures of Lie algebras, Lie coalgebras, Lie bialgebras and Lie quasibialgebras are presented as solutions of Maurer–Cartan
equations on corresponding governing differential graded Lie algebras using the big bracket construction of Kosmann–Schwarzbach.
This approach provides a definition of an L
∞-(quasi)bialgebra (strongly homotopy Lie (quasi)bialgebra). We recover an L
∞-algebra structure as a particular case of our construction. The formal geometry interpretation leads to a definition of an
L
∞ (quasi)bialgebra structure on V as a differential operator Q on V, self-commuting with respect to the big bracket. Finally, we establish an L
∞-version of a Manin (quasi) triple and get a correspondence theorem with L
∞-(quasi)bialgebras.
This paper is dedicated to Jean-Louis Loday on the occasion of his 60th birthday with admiration and gratitude. 相似文献
18.
Ángel Ballesteros Francisco J. Herranz Orlando Ragnisco Mariano Santander 《International Journal of Theoretical Physics》2008,47(3):649-663
The role of curvature in relation with Lie algebra contractions of the pseudo-orthogonal algebras so(p,q) is fully described by considering some associated symmetrical homogeneous spaces of constant curvature within a Cayley–Klein
framework. We show that a given Lie algebra contraction can be interpreted geometrically as the zero-curvature limit of some
underlying homogeneous space with constant curvature. In particular, we study in detail the contraction process for the three
classical Riemannian spaces (spherical, Euclidean, hyperbolic), three non-relativistic (Newtonian) spacetimes and three relativistic
((anti-)de Sitter and Minkowskian) spacetimes. Next, from a different perspective, we make use of quantum deformations of
Lie algebras in order to construct a family of spaces of non-constant curvature that can be interpreted as deformations of
the above nine spaces. In this framework, the quantum deformation parameter is identified as the parameter that controls the
curvature of such “quantum” spaces. 相似文献
19.
E. Kapuścik 《Czechoslovak Journal of Physics》2000,50(11):1279-1282
A Lie algebra unifying the noncanonical Lie algebra of quantum mechanical observables and the Lie algebra of the Galilei group
is constructed.
Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. 相似文献
20.
S. Majid 《Czechoslovak Journal of Physics》1997,47(12):1241-1250
We introduce anyonic Lie algebras in terms of structure constants. We provide the simplest examples and formulate some open
problems.
Presented at the 6th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 19–21 June
1997.
This paper is in final form and no version of it will be published elsewhere. 相似文献