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Algebra, Geometry, and Mathematical Physics 2010
- 2012
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Ingår i: Journal of Physics: Conference Series. - : IOP Publishing. - 1742-6596 .- 1742-6588.
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Samlingsverk (redaktörskap) (övrigt vetenskapligt/konstnärligt)abstract
- This proceedings volume presents results obtained by the participants of the 6th Baltic–Nordic workshop 'Algebra, Geometry, and Mathematical Physics (AGMP-6)' held at the Sven Lovén Centre for Marine Sciences in Tjärnö, Sweden on October 25–30, 2010. The Baltic–Nordic Network AGMP 'Algebra, Geometry, and Mathematical Physics' http://www.agmp.eu was created in 2005 on the initiative of two Estonian universities and two Swedish universities: Tallinn University of Technology represented by Eugen Paal (coordinator of the network), Tartu University represented by Viktor Abramov, Lund University represented by Sergei Silvestrov, and Chalmers University of Technology and the University of Gothenburg represented by Alexander Stolin. The goal was to promote international and interdisciplinary cooperation between scientists and research groups in the countries of the Baltic–Nordic region in mathematics and mathematical physics, with special emphasis on the important role played by algebra and geometry in modern physics, engineering and technologies. The main activities of the AGMP network consist of a series of regular annual international workshops, conferences and research schools. The AGMP network also constitutes an important educational forum for scientific exchange and dissimilation of research results for PhD students and Postdocs. The network has expanded since its creation, and nowadays its activities extend beyond countries in the Baltic–Nordic region to universities in other European countries and participants from elsewhere in the world. As one of the important research-dissimilation outcomes of its activities, the network has a tradition of producing high-quality research proceedings volumes after network events, publishing them with various international publishers.
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| 2. |
- Johannesson, Henrik, 1953, et al.
(författare)
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Quantum deformed Richardson-Gaudin model
- 2013
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Ingår i: Progress in Electromagnetics Research Symposium, PIERS 2013 Stockholm. - 1559-9450. - 9781934142264 ; , s. 789-793
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Konferensbidrag (refereegranskat)abstract
- The Richardson-Gaudin model describes strong pairing correlations of fermions confined to a finite chain. The integrability of the Hamiltonian allows for its eigenstates to be constructed algebraically. In this work, we show that quantum group theory provides a possibility to deform the Hamiltonian preserving integrability. More precisely, we use the so-called Jordanian r-matrix to deform the Hamiltonian of the Richardson-Gaudin model. In order to preserve its integrability, we need to insert a special nilpotent term into the auxiliary L-operator which generates integrals of motion of the system. Moreover, the quantum inverse scattering method enables us to construct the exact eigenstates of the deformed Hamiltonian. These states have a highly complex entanglement structure which require further investigation.
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| 3. |
- Kulish, Petr, et al.
(författare)
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Deformed Richardson-Gaudin model
- 2014
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Ingår i: Journal of Physics, Conference Series. - : IOP Publishing. - 1742-6588 .- 1742-6596. ; 532
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Tidskriftsartikel (refereegranskat)abstract
- The Richardson-Gaudin model describes strong pairing correlations of fermions confined to a finite chain. The integrability of the Hamiltonian allows the algebraic construction of its eigenstates. In this work we show that the quantum group theory provides a possibility to deform the Hamiltonian preserving integrability. More precisely, we use the so-called Jordanian r-matrix to deform the Hamiltonian of the Richardson-Gaudin model. In order to preserve its integrability, we need to insert a special nilpotent term into the auxiliary L-operator which generates integrals of motion of the system. Moreover, the quantum inverse scattering method enables us to construct the exact eigenstates of the deformed Hamiltonian. These states have a highly complex entanglement structure which require further investigation.
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| 4. |
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| 5. |
- Gekhtman, M., et al.
(författare)
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Poisson Structures Compatible with the Cluster Algebra Structure in Grassmannians
- 2012
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Ingår i: Letters in Mathematical Physics. - : Springer Science and Business Media LLC. - 0377-9017 .- 1573-0530. ; 100:2, s. 139-150
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Tidskriftsartikel (refereegranskat)abstract
- The present paper is a first step toward establishing connections between solutions of the classical Yang-Baxter equations and cluster algebras. We describe all Poisson brackets compatible with the natural cluster algebra structure in the open Schubert cell of the Grassmannian G(k)(n) and show that any such bracket endows G(k)(n) with a structure of a Poisson homogeneous space with respect to the natural action of SLn equipped with an R-matrix Poisson-Lie structure. The corresponding R-matrices belong to the simplest class in the Belavin-Drinfeld classification. Moreover, every compatible Poisson structure can be obtained this way.
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| 6. |
- Karolinsky, E., et al.
(författare)
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Equivariant quantization of Poisson homogeneous spaces and Kostant's problem
- 2014
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Ingår i: Journal of Algebra. - : Academic Press Inc.. - 0021-8693 .- 1090-266X. ; 409, s. 362-381
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Tidskriftsartikel (refereegranskat)abstract
- We find a partial solution to the longstanding problem of Kostant concerning description of the so-called locally finite endomorphisms of highest weight irreducible modules. The solution is obtained by means of its reduction to a far-reaching extension of the quantization problem. While the classical quantization problem consists in finding *product deformations of the commutative algebras of functions, we consider the case when the initial object is already a noncommutative algebra, the algebra of functions within q-calculus.
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| 7. |
- Kulish, Petr, et al.
(författare)
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Bethe ansatz for the deformed Gaudin model
- 2010
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Ingår i: Proceedings of the Estonian Academy of Sciences. - : Estonian Academy Publishers. - 1736-6046 .- 1736-7530. ; 59:4, s. 326-331
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Tidskriftsartikel (refereegranskat)
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| 8. |
- Makhlouf, A, et al.
(författare)
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Preface: Proceedings Algebra, Geometry and Mathematical Physics Conference, AGMP 2011 : Mulhouse, France, October 2011
- 2014
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Ingår i: Algebra, Geometry and Mathematical Physics AGMP, Mulhouse, France, October 2011 123. (Springer Proceedings in Mathematics and Statistics). - Berlin, Heidelberg : Springer Berlin Heidelberg. - 2194-1009. - 9783642553608
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Konferensbidrag (refereegranskat)
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| 9. |
- Montaner, F, et al.
(författare)
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Classification of Lie bialgebras over current algebras
- 2010
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Ingår i: Selecta Mathematica, New Series. - : Springer Science and Business Media LLC. - 1420-9020 .- 1022-1824. ; 16:4, s. 935-962
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we give a classification of Lie bialgebra structures on Lie algebras of type g[[x]] and g[x], where g is a simple complex finite dimensional Lie algebra
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| 10. |
- Paal, Eugen, 1954, et al.
(författare)
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3Quantum: Algebra, Geometry, Information
- 2014
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Ingår i: Journal of Physics Conference Series. - : IOP Publishing. - 1742-6588 .- 1742-6596. ; 532
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Konferensbidrag (refereegranskat)abstract
- The basic information about the international QQQ Conference 3Quantum: Algebra Geometry Information (Tallinn, July 2012) [ AstrAlgo cWeb 2012 QQQ II] is presented and the concise review of the QQQ Proceedings is given by the proceedings volume editors.
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