共查询到20条相似文献,搜索用时 15 毫秒
1.
Run-Qiang Jian 《Letters in Mathematical Physics》2013,103(8):851-863
In this letter, we use quantum quasi-shuffle algebras to construct Rota–Baxter algebras, as well as tridendriform algebras. We also propose the notion of braided Rota–Baxter algebras, the relevant object of Rota–Baxter algebras in a braided tensor category. Examples of such new algebras are provided using quantum multi-brace algebras in a category of Yetter–Drinfeld modules. 相似文献
2.
Ebrahimi-Fard Kurusch José M. Gracia-Bondía Frédéric Patras 《Letters in Mathematical Physics》2007,81(1):61-75
The word problem for an arbitrary associative Rota–Baxter algebra is solved. This leads to a noncommutative generalization
of the classical Spitzer identities. Links to other combinatorial aspects are indicated.
相似文献
3.
Michel Planat Anne-Céline Baboin Metod Saniga 《International Journal of Theoretical Physics》2008,47(4):1127-1135
The commutation relations of the generalized Pauli operators of a qubit–qutrit system are discussed in the newly established
graph-theoretic and finite-geometrical settings. The dual of the Pauli graph of this system is found to be isomorphic to the
projective line over the product ring
. A “peculiar” feature in comparison with two-qubits is that two distinct points/operators can be joined by more than one
line. The multi-line property is shown to be also present in the graphs/geometries characterizing two-qutrit and three-qubit
Pauli operators’ space and surmised to be exhibited by any other higher-level quantum system.
This work was partially supported by the Science and Technology Assistance Agency under the contract # APVT–51–012704, the
VEGA grant agency projects # 2/6070/26 and # 7012 (all from Slovak Republic), the trans-national ECO-NET project # 12651NJ
“Geometries over Finite Rings and the Properties of Mutually Unbiased Bases” (France) and by the CNRS–SAV Project # 20246
“Projective and Related Geometries for Quantum Information” (France/Slovakia). 相似文献
4.
5.
Run-Qiang Jian 《Letters in Mathematical Physics》2017,107(2):367-374
In this short note, we construct quasi-idempotent Rota–Baxter operators by quasi-idempotent elements and show that every finite dimensional Hopf algebra admits nontrivial Rota–Baxter algebra structures and tridendriform algebra structures. Several concrete examples are provided, including finite quantum groups and Iwahori–Hecke algebras. 相似文献
6.
This paper addresses several structural aspects of the insertion–elimination algebra \({\mathfrak{g}}\), a Lie algebra that can be realized in terms of tree-inserting and tree-eliminating operations on the set of rooted trees. In particular, we determine the finite-dimensional subalgebras of \({\mathfrak{g}}\), the automorphism group of \({\mathfrak{g}}\), the derivation Lie algebra of \({\mathfrak{g}}\), and a generating set. Several results are stated in terms of Lie algebras admitting a triangular decomposition and can be used to reproduce results for the generalized Virasoro algebras. 相似文献
7.
《Journal of Nonlinear Mathematical Physics》2013,20(3):325-341
Abstract In this paper we study generalized classes of volume preserving multidimensional integrable systems via Nambu–Poisson mechanics. These integrable systems belong to the same class of dispersionless KP type equation. Hence they bear a close resemblance to the self dual Einstein equation. All these dispersionless KP and dToda type equations can be studied via twistor geometry, by using the method of Gindikin’s pencil of two forms. Following this approach we study the twistor construction of our volume preserving systems. 相似文献
8.
The Lie–Rinehart algebra of a (connected) manifold ${\mathcal {M}}$ , defined by the Lie structure of the vector fields, their action and their module structure over ${C^\infty({\mathcal {M}})}$ , is a common, diffeomorphism invariant, algebra for both classical and quantum mechanics. Its (noncommutative) Poisson universal enveloping algebra ${\Lambda_{R}({\mathcal {M}})}$ , with the Lie–Rinehart product identified with the symmetric product, contains a central variable (a central sequence for non-compact ${{\mathcal {M}}}$ ) ${Z}$ which relates the commutators to the Lie products. Classical and quantum mechanics are its only factorial realizations, corresponding to Z = i z, z = 0 and ${z = \hbar}$ , respectively; canonical quantization uniquely follows from such a general geometrical structure. For ${z =\hbar \neq 0}$ , the regular factorial Hilbert space representations of ${\Lambda_{R}({\mathcal{M}})}$ describe quantum mechanics on ${{\mathcal {M}}}$ . For z = 0, if Diff( ${{\mathcal {M}}}$ ) is unitarily implemented, they are unitarily equivalent, up to multiplicity, to the representation defined by classical mechanics on ${{\mathcal {M}}}$ . 相似文献
9.
We develop the noncommutative geometry (bundles, connections etc.) associated to algebras that factorise into two subalgebras.
An example is the factorisation of matrices M
2(ℂ)=ℂℤ2·ℂℤ2. We also further extend the coalgebra version of theory introduced previously, to include frame resolutions and corresponding
covariant derivatives and torsions. As an example, we construct q-monopoles on all the Podleś quantum spheres S
2
q,s
.
Received: 25 September 1998 / Accepted: 23 February 2000 相似文献
10.
Boundary solutions to the quantum Yang–Baxter (qYB) equation are defined to be those in the boundary of (but not in) the variety of solutions to the modified qYB equation, the latter being analogous to the modified classical Yang–Baxter (cYB) equation. We construct, for a large class of solutions r to the modified cYB equation, explicit boundary quantizations, i.e., boundary solutions to the qYB equation of the form I + tr + t2r2 +. In the last section we list and give quantizations for all classical r-matrices in sl(3) sl(3). 相似文献
11.
Nigel Hitchin 《Communications in Mathematical Physics》2006,265(1):131-164
Using the idea of a generalized Kähler structure, we construct bihermitian metrics on CP2 and CP1×CP1, and show that any such structure on a compact 4-manifold M defines one on the moduli space of anti-self-dual connections on a fixed principal bundle over M. We highlight the role of holomorphic Poisson structures in all these constructions. 相似文献
12.
13.
Charles-Michel Marle 《Letters in Mathematical Physics》2009,90(1-3):3-21
We analyse articles by Lagrange and Poisson written two 200 years ago which are the foundation of present-day symplectic and Poisson geometry. 相似文献
14.
For a Lie algebra with Lie bracket got by taking commutators in a nonunital associative algebra
, let
be the vector space of tensors over
equipped with the Itô Hopf algebra structure derived from the associative multiplication in
. It is shown that a necessary and sufficient condition that the double product integral
satisfy the quantum Yang–Baxter equation over
is that
satisfy the same equation over the unital associative algebra
got by adjoining a unit element to
. In particular, the first-order coefficient r1 of r[h] satisfies the classical Yang–Baxter equation. Using the fact that the multiplicative inverse of
is
where
is the inverse of
in
we construct a quantisation of an arbitrary quasitriangular Lie bialgebra structure on
in the unital associative subalgebra of
consisting of formal power series whose zero order coefficient lies in the space
of symmetric tensors. The deformation coproduct acts on
by conjugating the undeformed coproduct by
and the coboundary structure r of
is given by
where
is the flip.Mathematical Subject Classification (2000). 53D55, 17B62 相似文献
15.
Let \({U_q(\widehat{\mathfrak g})}\) be the quantum affine algebra associated to a simply-laced simple Lie algebra \({\mathfrak{g}}\) . We examine the relationship between Dorey’s rule, which is a geometrical statement about Coxeter orbits of \({\mathfrak{g}}\) -weights, and the structure of q-characters of fundamental representations V i,a of \({U_q(\widehat{\mathfrak g})}\) . In particular, we prove, without recourse to the ADE classification, that the rule provides a necessary and sufficient condition for the monomial 1 to appear in the q-character of a three-fold tensor product \({V_{i,a}\otimes V_{j,b}\otimes V_{k,c}}\) . 相似文献
16.
N. P. Landsman 《Communications in Mathematical Physics》2001,222(1):97-16
It is well known that a measured groupoid G defines a von Neumann algebra W
*(G), and that a Lie groupoid G canonically defines both a C
*-algebra C
*(G) and a Poisson manifold A
*(G). We construct suitable categories of measured groupoids, Lie groupoids, von Neumann algebras, C
*-algebras, and Poisson manifolds, with the feature that in each case Morita equivalence comes down to isomorphism of objects.
Subsequently, we show that the maps G↦W
*(G), G↦C
*(G), and G↦A
*(G) are functorial between the categories in question. It follows that these maps preserve Morita equivalence.
Received: 6 December 2000 / Accepted: 19 April 2001 相似文献
17.
Alexander Chervov Gregorio Falqui Leonid Rybnikov 《Letters in Mathematical Physics》2010,91(2):129-150
Gaudin algebras form a family of maximal commutative subalgebras in the tensor product of n copies of the universal enveloping algebra \({U(\mathfrak {g})}\) of a semisimple Lie algebra \({\mathfrak {g}}\). This family is parameterized by collections of pairwise distinct complex numbers z 1, . . . , z n . We obtain some new commutative subalgebras in \({U(\mathfrak {g})^{\otimes n}}\) as limit cases of Gaudin subalgebras. These commutative subalgebras turn to be related to the Hamiltonians of bending flows and to the Gelfand–Tsetlin bases. We use this to prove the simplicity of spectrum in the Gaudin model for some new cases. 相似文献
18.
Explicit formulas for the symmetrizer and the antisymmetrizer of the Birman–Wenzl–Murakami algebras BWM(r,q)
n
are given. 相似文献
19.
Cλ-Extended Oscillator Algebras and Some of Their Deformations and Applications to Quantum Mechanics
C-extended oscillator algebras generalizing the Calogero—Vasiliev algebra,where C is the cyclic group of order , are studied both from mathematical andapplied viewpoints. Casimir operators of the algebras are obtained and used toprovide a complete classification of their unitary irreducible representations underthe assumption that the number operator spectrum is nondegenerate. Deformedalgebras admitting Casimir operators analogous to those of their undeformedcounterparts are looked for, yielding three new algebraic structures. One of themincludes the Brzezi´nski et al. deformation of the Calogero—Vasiliev algebra as aspecial case. In its bosonic Fock-space representation, the realization ofC-extended oscillator algebras as generalized deformed oscillator ones is shown toprovide a bosonization of several variants of supersymmetric quantum mechanics:parasupersymmetric quantum mechanics of order p = – 1 for any , as wellas pseudosupersymmetric and orthosupersymmetric quantum mechanics of ordertwo for = 3. 相似文献
20.
We use a generalized Ricci tensor, defined for generalized metrics in Courant algebroids, to show that Poisson–Lie T-duality is compatible with the 1-loop renormalization group flow. 相似文献