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QUANTUM SYMMETRIES OF HIGHER COXETERDYNKIN GRAPHS. A Noncommutative Case: The D3 Graph of SU(3) System
"... The purpose of this contribution is to show how quantum geometry of higher Coxeter graphs of SU(N) type gives a common algebraic formulation for both RCFT and quantum groupoı̈ds. These apparently two different fields are hardly studied by wide communities of physicists and mathematicians. To carry o ..."
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out this formulation we determine all Nimreps describing CFT and weak Hopf algebra structures based on combinatorial data of graphs. We will pay attention to a particular case: the D 3 orbifold graph of SU(3) system for which the algebra of quantum symmetries is noncommutative.
NECESSARY CONDITIONS INVOLVING LIE BRACKETS FOR IMPULSIVE OPTIMAL CONTROL PROBLEMS; THE COMMUTATIVE CASE
, 2012
"... ..."
SOLUTION OF RIEMANN–HILBERT PROBLEM RELATED TO WIENER–HOPF MATRIX FACTORIZATION PROBLEM USING ORDINARY DIFFERENTIAL EQUATIONS IN THE COMMUTATIVE CASE
"... A matrix factorization problem is considered. The matrix is algebraic and belongs to the Jones– Moiseev class. A new method of factorization is proposed. The matrix factorization problem is reduced to a Riemann–Hilbert problem using Hurd’s method. The Riemann–Hilbert problem is embedded into a famil ..."
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A matrix factorization problem is considered. The matrix is algebraic and belongs to the Jones– Moiseev class. A new method of factorization is proposed. The matrix factorization problem is reduced to a Riemann–Hilbert problem using Hurd’s method. The Riemann–Hilbert problem is embedded into a family of Riemann–Hilbert problems indexed by a variable b taking values on a halfline. A linear ordinary differential equation (ODE1) with respect to b is derived. The coefficient of this equation remains unknown at this step. Finally, the coefficient of the ODE1 is computed. For this, it is proven that this coefficient obeys a nonlinear ordinary differential equation (ODE2) on a halfline. Thus, the numerical procedure of matrix factorization becomes reduced to two runs of solving ordinary differential equations on a halfline: first ODE2 for the coefficient of ODE1, and then ODE1 for the unknown function. The efficiency of the new method is demonstrated on some examples. 1.
∗I would like to express my gratitude to Professor A. Mallios for suggesting the topic.
"... differentials in Amodules: noncommutative and commutative cases ..."
Noncommutative Burkholder/Rosenthal inequalities
 Ann. Probab
, 2000
"... Abstract. We show norm estimates for the sum of independent random variables in noncommutative Lp spaces for 1 < p < ∞ following previous work by the authors. These estimates generalize Rosenthal’s inequalities in the commutative case. Among other applications, we derive a formula for pnorm o ..."
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Cited by 84 (34 self)
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Abstract. We show norm estimates for the sum of independent random variables in noncommutative Lp spaces for 1 < p < ∞ following previous work by the authors. These estimates generalize Rosenthal’s inequalities in the commutative case. Among other applications, we derive a formula for p
Natural associativity and commutativity
 Rice University Studies
, 1963
"... the "general associative law, " which states that any two iterated products of the same factors in the same order are equal, irrespective of the arrangement of parentheses. Here we are concerned with an associativity given by an isomorphism a: A(BC) G (AB)C; more exactly, with the case ..."
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Cited by 96 (1 self)
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the "general associative law, " which states that any two iterated products of the same factors in the same order are equal, irrespective of the arrangement of parentheses. Here we are concerned with an associativity given by an isomorphism a: A(BC) G (AB)C; more exactly, with the case
Commutative geometries are spin manifolds
 Rev. Math. Phys
"... In [1], Connes presented axioms governing noncommutative geometry. He went on to claim that when specialised to the commutative case, these axioms recover spin or spin c geometry depending on whether the geometry is “real ” or not. We attempt to flesh out the details of Connes ’ ideas. As an illustr ..."
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Cited by 13 (2 self)
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In [1], Connes presented axioms governing noncommutative geometry. He went on to claim that when specialised to the commutative case, these axioms recover spin or spin c geometry depending on whether the geometry is “real ” or not. We attempt to flesh out the details of Connes ’ ideas
An ergodic Szemer'edi theorem for commuting transformations
 J. Analyse Math
, 1979
"... The classical Poincar6 recurrence theorem asserts that under the action of a measure preserving transformation T of a finite measure space (X, ~, p.), every set A of positive measure recurs in the sense that for some n> 0,/z (T'A n A)> 0. In [1] this was extended to multiple recurrence: ..."
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Cited by 113 (2 self)
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, implies van der Waerden's theorem on arithmetic progressions for partitions of the integers. Now in this case a virtually identical argument shows that the topological result is true for any k commuting transformations. This would lead one to expect that the measure theoretic result is also true
DISCRETE NONCOMMUTATIVE INTEGRABILITY: THE PROOF
, 909
"... Abstract. We prove a conjecture of Kontsevich regarding the solutions of rank two recursion relations for noncommutative variables which, in the commutative case, reduce to rank two cluster algebras of affine type. The conjecture states that solutions are positive Laurent polynomials in the initial ..."
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Abstract. We prove a conjecture of Kontsevich regarding the solutions of rank two recursion relations for noncommutative variables which, in the commutative case, reduce to rank two cluster algebras of affine type. The conjecture states that solutions are positive Laurent polynomials
On fusion categories
 Annals of Mathematics
"... Abstract. In this paper we extend categorically the notion of a finite nilpotent group to fusion categories. To this end, we first analyze the trivial component of the universal grading of a fusion category C, and then introduce the upper central series ofC. For fusion categories with commutative Gr ..."
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Cited by 216 (32 self)
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Abstract. In this paper we extend categorically the notion of a finite nilpotent group to fusion categories. To this end, we first analyze the trivial component of the universal grading of a fusion category C, and then introduce the upper central series ofC. For fusion categories with commutative
Results 11  20
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