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1.
Hong Wei Yang Bao Shu Yin Yong Fang 《International Journal of Theoretical Physics》2011,50(3):671-681
A class of new Lie algebra B
3 is constructed, which is far different from the known Lie algebra A
n−1. Based on the corresponding loop algebra [(B3)\tilde]\tilde{B_{3}}, the generalized mKdV hierarchy is established. In order to look for the Hamiltonian structure of such integrable system,
a generalized trace functional of matrices is introduced, whose special case is just the well-known trace identity. Finally,
its expanding integrable model is worked out by use of an enlarged Lie algebra. 相似文献
2.
Embeddings of the CAR (canonical anticommutation relations) algebra of fermions into the Cuntz algebra ?2 (or ?2
d
more generally) are presented by using recursive constructions. As a typical example, an embedding of CAR onto the U(1)-invariant subalgebra of ?2 is constructed explicitly. Generalizing this construction to the case of ?2
p
, an embedding of CAR onto the U(1)-invariant subalgebra of ?2
p
is obtained. Restricting a permutation representation of the Cuntz algebra, we obtain the Fock representation of CAR. We
apply the results to embed the algebra of parafermions of order p into ?2
p
according to Green's ansatz.
Received: 3 September 2001 / Accepted: 19 January 2002 相似文献
3.
Haisheng Li 《Communications in Mathematical Physics》2005,259(2):391-411
To every vertex algebra V we associate a canonical decreasing sequence of subspaces and prove that the associated graded vector space gr(V) is naturally a vertex Poisson algebra, in particular a commutative vertex algebra. We establish a relation between this decreasing sequence and the sequence Cn introduced by Zhu. By using the (classical) algebra gr(V), we prove that for any vertex algebra V, C2-cofiniteness implies Cn-cofiniteness for all n≥2. We further use gr(V) to study generating subspaces of certain types for lower truncated ℤ-graded vertex algebras.Partially supported by an NSA grant 相似文献
4.
Zhixiang Wu 《International Journal of Theoretical Physics》2011,50(4):1220-1244
In present paper we define a new kind of weak quantized enveloping algebra of Borcherds superalgebras. We denote this algebra
by wUqt(G)wU_{q}^{\tau}(\mathcal{G}). It is a noncommutative and noncocommutative weak graded Hopf algebra under some additional condition. It has a homomorphic
image which is isomorphic to the usual quantum enveloping algebra Uq(G)U_{q}(\mathcal{G}) of G\mathcal{G}. 相似文献
5.
Jintai Ding 《Letters in Mathematical Physics》1996,38(2):177-183
We define the crystal algebra, an algebra which has a base of elements of crystal bases of a quantum group. The multiplication is defined by the tensor product rule of crystal bases. A universal n-colored crystal algebra is defined. We study the relation between those algebras and the tensor algebras of the crystal algebra of U
q
(sl(2)) and give a presentation by generators and relations for the case of U
q
(sl(n)). 相似文献
6.
Bernhard Drabant Branislav Jurčo Michael Schlieker Wolfgang Weich Bruno Zumino 《Letters in Mathematical Physics》1992,26(2):91-96
We derive the equivalence of the complex quantum enveloping algebra and the algebra of complex quantum vector fields for the Lie algebra types A
n
, B
n
, C
n
, and D
n
by factorizing the vector fields uniquely into a triangular and a unitary part and identifying them with the corresponding elements of the algebra of regular functionals.Humboldt Fellow. 相似文献
7.
Abdullah Algin 《Czechoslovak Journal of Physics》2002,52(9):1011-1019
A two-parameter deformed N = 2 SUSY algebra is constructed by using the q-deformed bosonic and fermionic Newton oscillator algebras. The Fock space representation of the (q
1,q
2)-deformed N = 2 SUSY algebra is analyzed. The comparison between the algebra constructed and earlier versions of deformed N = 2 SUSY algebras is also made. 相似文献
8.
A. Ouarab 《International Journal of Theoretical Physics》2000,39(6):1609-1617
An n-dimensional fractional supersymmetry theory is algebraically constructedon the n-dimensional multicomplex space M
n. By emphasizing its appearanceas a special case of generalized Clifford algebra (GCA), we formulate the fractional superspace FM
n
through a generalized Grassmann algebra (GGA) and constructthe generators and the covariant derivative of FSUSY on FM
n
. The generatorsof FSUSY are extended to get n copies of the fractional centerlesssuper-Virasoro algebra. 相似文献
9.
A. U. Klimyk 《Czechoslovak Journal of Physics》1998,48(11):1395-1400
A nonstandard q-deformed Euclidean algebra U
q(iso
n
), based on the definition of the twisted q-deformed algebra U
qson) (different from the Drinfeld–Jimbo algebra U
q(so
n
)), is defined. Infinite dimensional representations R of U
q(iso
n
) are described. Explicit formulas for operators of these representations in the orthonormal basis are given. The spectra of the operators R(T
n) corresponding to a q-analogue of the infinitesimal operator of shifts along the n-th axis are described. Contrary to the case of the classical Euclidean Lie algebra iso
n
, these spectra are discrete and spectral points have one point of accumulation. 相似文献
10.
In this paper we construct a newN = 6 superconformal algebra which extends the Virasoro algebra by theSO
6 current algebra, by 6 odd primary fields of conformal weight 3/2 and by 10 odd primary fields of conformal weight 1/2. The
commutation relations of this algebra, which we will refer to asCK
6, are represented by short distance operator product expansions (OPE). We constructCK
6, as a subalgebra of theSO(6) superconformal algebra K6, thus giving it a natural representation as first order differential operators on the circle withN = 6 extended symmetry. We show thatCK
6 has no nontrivial central extensions.
Partially supported by NSC grant 85-2121-M-006-019 of the ROC.
Partially supported by NSF grant DMS-9622870. 相似文献
11.
Atsushi Matsuo 《Communications in Mathematical Physics》2001,224(3):565-591
Formulae expressing the trace of the composition of several (up to five) adjoint actions of elements of the Griess algebra
of a vertex operator algebra are derived under certain assumptions on the action of the automorphism group. They coincide,
when applied to the moonshine module V
, with the trace formulae obtained in a different way by S. Norton, and the spectrum of some idempotents related to 2A, 2B,
3A and 4A elements of the Monster is determined by the representation theory of the Virasoro algebra at c= 1/2, the W
3 algebra at c= 4/5 or the W
4 algebra at c= 1. The generalization to the trace function on the whole space is also given for the composition of two adjoint actions,
which can be used to compute the McKay-Thompson series for a 2A involution of the Monster.
Received: 24 July 2000 / Accepted: 15 June 2001 相似文献
12.
We establish an explicit algebra isomorphism between the quantum reflection algebra for the Uq([^(sl2)]) R{U_q(\widehat{sl_2}) R}-matrix and a new type of current algebra. These two algebras are shown to be two realizations of a special case of tridiagonal
algebras (q-Onsager). 相似文献
13.
Based on the Lie algebra A
1, the integrable Broer-Kaup-Kupershmidt (BKK) system is revisited. The bi-Hamiltonian structure is constructed by the trace
identity. Two extensions of the Lie algebra A
1 are considered, i.e., the non-semi-simple Lie algebra of 4×4 matrix and the super-Lie algebra of 3×3 matrix, from which two
hierarchies of soliton equations related to BKK system are given. With the aid of the generalized trace identity and the super-trace
identity, the Hamiltonian and super-Hamiltonian structures of the resulting systems are constructed. 相似文献
14.
The algebra dual to Woronowicz's deformation of the two-dimensional Euclidean group is constructed. The same algebra is obtained from SU
q
(2) via contraction on both the group and algebra levels. 相似文献
15.
Cao Li-ke Liang Hong Peng Dan-tao Yang Tao Yue Rui-hong 《Frontiers of Physics in China》2007,2(2):234-237
Gaudin model is a very important integrable model in both quantum field theory and condensed matter physics. The integrability
of Gaudin models is related to classical r-matrices of simple Lie algebras and semi-simple Lie algebra. Since most of the constructions of Gaudin models works concerned
mainly on rational and trigonometric Gaudin algebras or just in a particular Lie algebra as an alternative to the matrix entry
calculations often presented, in this paper we give our calculations in terms of a basis of the typical Lie algebra, A
n
, B
n
, C
n
, D
n
, and we calculate a classical r-matrix for the elliptic Gaudin system with spin.
相似文献
16.
17.
Bruno Gruber 《Letters in Mathematical Physics》1982,6(5):329-334
In this article two theorems are given which permit, together with the concept of a representation vector diagram, to classify all (linear) finite-dimensional representations of the algebra and group E
2 which are induced by a master representation on the place of the universal enveloping algebra of the algebra E
2. Apart from a classification of the finite-dimensional representations, the two theorems make it possible to obtain the matrix elements of these representations for both, algebra and group, in explicit form. The material contained in this letter forms part of an analysis of indecomposable (finite- and infinite-dimensional) representations of the algebra and group E
2 which is contained in Reference [1]. No proofs will be given in this letter. We refer instead to [1]. 相似文献
18.
A. P. Isaev 《Letters in Mathematical Physics》1995,34(4):333-341
We show that the differential complex
B
over the braided matrix algebra BM
q
(N) represents a covariant comodule with respect to the coaction of the Hopf algebra
A
which is a differential extension of GL
q
(N). On the other hand, the algebra
A
is a covariant braided comodule with respect to the coaction of the braided Hopf algebra
B
. Geometrical aspects of these results are discussed. 相似文献
19.
V. K. B. Kota 《Pramana》2003,60(1):59-74
It is shown that the proton-neutron interacting boson model (pnIBM) admits new symmetry limits withO(12) algebra which breakF spin but preserves theF
z quantum numberM
F. The generators ofO(12) are derived and the quantum numberU ofO(12) for a given boson numberN is determined by identifying the corresponding quasi-spin algebra. TheO(12) algebra generates two symmetry schemes and for both of them, complete classification of the basis states and typical
spectra are given. With theO(12) algebra identified, complete classification of pnIBM symmetry limits with goodM
F is established. 相似文献
20.
E. Frenkel N. Reshetikhin M.A. Semenov-Tian-Shansky 《Communications in Mathematical Physics》1998,192(3):605-629
We propose a q-difference version of the Drinfeld-Sokolov reduction scheme, which gives us q-deformations of the classical -algebras by reduction from Poisson-Lie loop groups. We consider in detail the case of SL
2
. The nontrivial consistency conditions fix the choice of the classical r-matrix defining the Poisson-Lie structure on the loop group LSL
2
, and this leads to a new elliptic classical r-matrix. The reduced Poisson algebra coincides with the deformation of the classical Virasoro algebra previously defined in
[19]. We also consider a discrete analogue of this Poisson algebra. In the second part [31] the construction is generalized
to the case of an arbitrary semisimple Lie algebra.
Received: 20 April 1997 / Accepted: 22 July 1997 相似文献