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An analogue of the Conjecture of Dixmier is true for the algebra of polynomial integro-differential operators
Conjecture algebra polynomial integro-differential operators
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2010/11/19
Let $A_1:=K\langle x, \frac{d}{dx} \rangle$ be the Weyl algebra and $\mI_1:= K\langle x, \frac{d}{dx}, \int \rangle$ be the algebra of polynomial integro-differential operators over a field $K$ of cha...
Integrable Henon-Heiles Hamiltonians: a Poisson algebra approach
Integrable Henon-Heiles Hamiltonians Poisson algebra approach
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2010/11/19
The three integrable two-dimensional Henon-Heiles systems and their integrable perturbations are revisited. A family of new integrable perturbations is found, and N-dimensional completely integrable ...
The algebra of integro-differential operators on an affine line and its modules
algebra integro-differential operators affine line
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2010/11/19
For the algebra $\mI_1= K\langle x, \frac{d}{dx}, \int \rangle$ of polynomial integro-differential operators over a field $K$ of characteristic zero, a classification of simple modules is given. It i...
Operator algebra quantum groups of universal gauge groups
Operator algebra quantum groups universal gauge groups
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2010/11/11
In this paper, we quantize universal gauge groups such as SU(\infty), in the sigma-C*-algebra setting. More precisely, we propose a concise definition of sigma-C*-quantum groups and explain the conce...
Classification of Harish-Chandra modules over some Lie algebras and superconformal algebras related to the Virasoro algebra
Harish-Chandra modules Lie algebras
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2010/11/22
In this paper, we provide a uniform method to thoroughly classify all Harish-Chandra modules over some Lie algebras and superconformal algebras related to the Virasoro algebras. We first classify suc...
The Gelfand spectrum of a noncommutative C*-algebra: a topos-theoretic approach
Gelfand spectrum noncommutative C*-algebra topos-theoretic approach
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2010/11/11
We compare two influential ways of defining a generalized notion of space. The first, inspired by Gelfand duality, states that the category of 'noncommutative spaces' is the opposite of the category o...
Boundary quotients of the Toeplitz algebra of the affine semigroup over the natural numbers
Boundary quotients Toeplitz algebra affine semigroup natural numbers
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2010/12/8
We study the Toeplitz algebra T (N ⋊ N×) and three quotients of this algebra: the C-algebra QN recntly introduced by Cuntz, and two new ones, which we call the additive and multiplicative bound...
Reflection algebras is a class of algebras associated with integrable models with boundaries. The coefficients of Sklyanin determinant generate the center of reflection algebra. We give a combinatoria...
Extending PT symmetry from Heisenberg algebra to E2 algebra
Extending PT symmetry Heisenberg algebra E2 algebra
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2010/10/27
The E2 algebra has three elements, J, u, and v, which satisfy the commutation relations [u; J] = iv, [v; J] = iu, [u; v] = 0. We can construct the Hamiltonian H = J2 +gu, where g is a real p...
A new calculus of planar diagrams involving diagrammatics for biadjoint func-tors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothend...
Relative homological algebra in categories of representations of infinite quivers
cover envelope torsion free flat representations of a quiver
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2010/11/26
In the first part of this paper, we prove the existence of torsion
free covers in the category of representations of quivers, (Q,R-Mod),for a wide class of quivers included in the class of the so-cal...
Products of Geck-Rouquier conjugacy classes and the Hecke algebra of composed permutations
Iwahori-Hecke algebras Geck-Rouquier conjugacy classes symmetric functions
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2010/12/9
We show the q-analog of a well-known result of Farahat and Higman: in the center of the Iwahori-Hecke algebraHn,q, if (a μ(n, q)) is the set of structure constants involved in the product of two G...
M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra
Formality Deformation Quantization Operads
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2010/12/1
We show that the zeroth cohomology of Kontsevich’s graph complex is isomorphic to the Grothendieck-Teichm¨uller Lie algebra grt. The map is explicitly described.
Extending PT symmetry from Heisenberg algebra to E2 algebra
Extending PT symmetry Heisenberg algebra E2 algebra
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2010/12/15
The E2 algebra has three elements, J, u, and v, which satisfy the commutation relations [u; J] = iv, [v; J] = iu, [u; v] = 0. We can construct the Hamiltonian H = J2 +gu, where g is a real p...
We construct a vertex algebra of central charge 26 from a lattice orbifold vertex operator algebra of central charge 12. The BRST-cohomology group of this vertex algebra is a new generalized Kac-Moody...