2 edition of **Integrable systems associated with elliptic algebras** found in the catalog.

Integrable systems associated with elliptic algebras

A. Odesskii

- 120 Want to read
- 20 Currently reading

Published
**2004**
by Kyōto Daigaku Sūri Kaiseki Kenkyūjo in Kyoto, Japan
.

Written in

**Edition Notes**

Statement | by A. Odesskii and V. Rubtsov. |

Series | RIMS -- 1476 |

Contributions | Rubtsov, V., Kyōto Daigaku. Sūri Kaiseki Kenkyūjo. |

Classifications | |
---|---|

LC Classifications | MLCSJ 2008/00046 (Q) |

The Physical Object | |

Pagination | 24 p. ; |

Number of Pages | 24 |

ID Numbers | |

Open Library | OL16447110M |

LC Control Number | 2008554199 |

This clarifies the role of (twisted) affine Kac-Moody algebras in elliptic Calogero-Moser systems and allows for a natural geometric con- struction of Lax operators for these systems. We elaborate on the connection of the associated Hamiltonians to superpotentials for N = 1∗ deformations of N = 4 supersymmetric gauge theory, and argue how non. *immediately available upon purchase as print book shipments may be delayed due to the COVID crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version.

First Workshop on Integrable Systems, 2 December Second Workshop on Integrable Systems, 4 - 5 December Third Workshop on Integrable Systems, 3 - 4 December Fourth Workshop on Integrable Systems, 1 - 2 December Registration. Register by emailing the organisers at: [email protected] Registrations close on 1. Audio Books & Poetry (III) An introduction to mechanical Hamiltonian integrable systems, such as the Toda and Calogero-Moser systems associated with general Lie algebras; a review of the recently constructed Lax pairs with spectral parameter for twisted and untwisted elliptic Calogero-Moser systems; (IV) A review of recent solutions of the.

Recent developments in the theory of infinite dimensional algebras and their applications to quantum integrable systems are reviewed by some of the leading experts in the field. The volume will be of interest to a broad audience from graduate students to researchers in . Khemar (U. Henri Poincare Nancy, France) studies all the elliptic integrable systems, that is, the family of all the m-th elliptic integrable systems associated to .

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Integrable systems associated with elliptic algebras to study the bi-hamiltonian structures giving the algebra q2m+1(E) using the results of Gelfand-Zakharevich ([33]) on the geometry of bi-hamiltonian systems in the case of odd-dimensional Poisson manifolds.

The precise quantum version of these systems. We construct some new Integrable Systems (IS) both classical and quantum associated with elliptic algebras. Our constructions are partly based on the algebraic integrability mechanism given by the. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract.

We construct some new Integrable Systems Integrable systems associated with elliptic algebras book both classical and quantum associated with elliptic algebras.

Our constructions are partly based on the algebraic integrability mechanism given by the existence of commuting families in skew fields and partly- on the internal properties of the elliptic algebras.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We construct new integrable systems (IS), both classical and quantum, associated with elliptic algebras. Our constructions are based both on a construction of commuting families in skew fields and on properties of the elliptic algebras and their representations.

We give some examples showing how these IS are. We construct some new Integrable Systems (IS) both classical and quantum associated with elliptic algebras. Our constructions are partly based on the algebraic integrability mechanism given by the existence of commuting families in skew fields and partly - on the internal properties of the elliptic algebras and their representations.

We give some examples to make an evidence how these IS are Cited by: 4. Still, some points remain obscure from the point of view of Hopf algebras. In particular, integrable models associated with elliptic curves are still poorly understood.

We propose her an elliptic version of quantum groups, based on the relation to conformal field theory, which hopefully will be helpful to complete the picture. INTEGRABLE SYSTEMS ASSOCIATED WITH ELLIPTIC ALGEBRAS 5 Mi(M0)−1Mj = Mj(M0)−1Mi (2) Bij(M0)−1Bkj = Bik(M0)−1Bij, (3) where Bij is the co-factor of the matrix element bi j, 0 ≤ i,j ≤ n.

Theorem can be reformulated to give the following result Corollary Let A be an algebra, (f i,j)0≤i≤n,1≤j≤n be elements of A such that f.

Integrable systems associated with elliptic algebras (pp. pdf) Soichi Okada: Generalizations of Cauchy's Determinant Identity and Schur's Pfaffian Identity (pp. pdf) M.A. Olshanetsky and A.V. Zotov: Isomonodromic problems on elliptic curve, rigid tops and reflection equations (pp. pdf) Yas-Hiro Quano.

In the context of differential equations to integrate an equation means to solve it from initial ingly, an integrable system is a system of differential equations whose behavior is determined by initial conditions and which can be integrated from those initial conditions. Many systems of differential equations arising in physics are integrable.

INTEGRABLE SYSTEMS ASSOCIATED WITH ELLIPTIC ALGEBRAS 5 Seiberg-Witten integrable systems associated with a hyperelliptic spectral curves in [35]. The important step in the demonstration of the is the following ”triangle” relations which are similar to the usual Yang -Baxter relation: Mi(M 0) −1Mj = Mj(M) Mi (2) Bij(M0)−1Bkj = Bik.

Integrable systems associated with elliptic algebras Submitted by Emmanuel Lemoine on Thu, 12/05/ - Titre Integrable systems associated with elliptic algebras Type de publication Chapitre Type Ouvrage scientifique Année Langue Anglais Pagination 81 - Volume 12 Titre de l'ouvrage Quantum Groups.

the point of view of Hopf algebras. In particular, integrable models associated with elliptic curves are still poorly understood. We propose here an elliptic version of quantum groups, based on the relation to conformal ﬁeld theory, which hopefully will be helpful to complete the picture.

But before going to the elliptic case, let us remind. Abstract. Abstract. We construct some new integrable systems (IS), both classical and quantum associated with elliptic algebras. Our constructions are partly based on a construction of commuting families in skew fields and partly- on properties of the elliptic algebras and their representations.

These directions were motivated by Sklyanin's work [35] on quantum integrable systems, in which he introduced the algebras now known as 4-dimensional Sklyanin algebras and studied their. We construct some new Integrable Systems (IS) both classical and quantum associated with elliptic algebras.

Our constructions are partly based on the algebraic. Chapter 2. m-th elliptic integrable system associated to a k'-symmetric space 27 38; Definition of G (even when does not integrate in G) 27 38; Finite order Lie algebra automorphisms 28 39; The even case: k'=2k 28 39; The odd case: k'=2k+1 30 41; Definitions and general properties of the m-th elliptic system 31 This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant.

While treating the material at an elementary level, the book also highlights many recent developments. 5. Hyperelliptic integrable system on rational surface Integrable system associated with rational elliptic surface. If the polynomials f(x) and g(x) in the Weierstrass model of elliptic K3 surfaces are replaced by polynomials of degree 4 and 6, respectively, the outcome is an rational elliptic surface.

book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship between vertex algebras and the geometry of algebraic curves.

The notion of a vertex algebra is introduced in the book in a coordinate-independent way, allowing the authors to give global geometric meaning to vertex operators on arbitrary. We consider nonlinear recurrences generated from cluster mutations applied to quivers that have the property of being cluster mutation-periodic with period 1.

Such quivers were completely classified by Fordy and Marsh, who characterised them in terms of the skew-symmetric matrix that defines the quiver.

The associated nonlinear recurrences are equivalent to birational maps, and we. Integrable Systems and Algebraic Geometry. Proceedings of the Taniguchi SymposiumRokko Oriental Hotel, Kobe Notes on the Flat Structures Associated with Simple and Simply Elliptic Singularities Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras.

Space, Time and Matter. Using the technique of the classical r-matrices and quantum Lax operators we construct the most general form of quantum integrable multi-boson and spin-multi-boson models associated with linear Lax algebras and sl (2) ⊗ sl (2)-valued classical non-dynamical r-matrices with spectral consider example of non-skew-symmetric elliptic r-matrix and explicitly obtain one- .Book a campus tour; Living at Brock; Smart Start; More information A.

Odesskii, V. Rubtsov, Integrable systems associated with elliptic algebras. The proceedings of the Workshop on Elliptic Integrable Systems, Rokko Lectures in Mathematics, N 18, Eds.

M. Noumi and K. Takasaki, Preprints • E. V. Ferapontov, A. V. Odesskii.