Search results for "REPRESENTATION"
showing 10 items of 1710 documents
An uncountable family of almost nilpotent varieties of polynomial growth
2017
A non-nilpotent variety of algebras is almost nilpotent if any proper subvariety is nilpotent. Let the base field be of characteristic zero. It has been shown that for associative or Lie algebras only one such variety exists. Here we present infinite families of such varieties. More precisely we shall prove the existence of 1) a countable family of almost nilpotent varieties of at most linear growth and 2) an uncountable family of almost nilpotent varieties of at most quadratic growth.
Isometric dilations and đ»^{â} calculus for bounded analytic semigroups and Ritt operators
2017
We show that any bounded analytic semigroup on L p L^p (with 1 > p > â 1>p>\infty ) whose negative generator admits a bounded H â ( ÎŁ Ξ ) H^{\infty }(\Sigma _\theta ) functional calculus for some Ξ â ( 0 , Ï 2 ) \theta \in (0,\frac {\pi }{2}) can be dilated into a bounded analytic semigroup ( R t ) t â©Ÿ 0 (R_t)_{t\geqslant 0} on a bigger L p L^p -space in such a way that R t R_t is a positive contraction for any t â©Ÿ 0 t\geqslant 0 . We also establish a discrete analogue for Ritt operators and consider the case when L p L^p -spaces are replaced by more general Banach spaces. In connection with these functional calculus issues, we study isometric dilations of bounded continuous repâŠ
Riemann-Hilbert approach to the time-dependent generalized sine kernel
2011
We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of integrable models described by a six-vertex R-matrix. This series representation opens a systematic way for the computation of the long-time, long-distance asymptotic expansion for the correlation functions of the aforementioned integrable models away from their free fermion point. Our method builds on a RiemannâHilbert based analysis.
Indecomposable sets of finite perimeter in doubling metric measure spaces
2020
We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak $(1,1)$-Poincar\'{e} inequality. The two main results we obtain are a decomposition theorem into indecomposable sets and a characterisation of extreme points in the space of BV functions. In both cases, the proof we propose requires an additional assumption on the space, which is called isotropicity and concerns the Hausdorff-type representation of the perimeter measure.
Possible extensions of the noncommutative integral
2011
In this paper we will discuss the problem of extending a trace Ï defined on a dense von Neumann subalgebra \(\mathfrak{M}\) of a topological *-algebra \({\mathfrak{A}}\) to some subspaces of \({\mathfrak{A}}\). In particular, we will prove that extensions of the trace Ï that go beyond the space L1(Ï) really exist and we will explicitly construct one of these extensions. We will continue the analysis undertaken in Bongiorno et al. (Rocky Mt. J. Math. 40(6):1745â1777, 2010) on the general problem of extending positive linear functionals on a *-algebra.
Unitary Representations of U q (đ°đ©}(2,â)),¶the Modular Double and the Multiparticle q -Deformed¶Toda Chain
2002
The paper deals with the analytic theory of the quantum q-deformed Toda chains; the technique used combines the methods of representation theory and the Quantum Inverse Scattering Method. The key phenomenon which is under scrutiny is the role of the modular duality concept (first discovered by L. Faddeev) in the representation theory of noncompact semisimple quantum groups. Explicit formulae for the Whittaker vectors are presented in terms of the double sine functions and the wave functions of the N-particle q-deformed open Toda chain are given as a multiple integral of the MellinâBarnes type. For the periodic chain the two dual Baxter equations are derived.
Unitary Representations of the Modular and Two-Particle Q-Deformed Toda Chains
2001
The paper deals with the analytic theory of the quantum two-particle q-deformed Toda chains. This is the simplest nontrivial example clarifying the role of the modular duality concept (first discovered by L.Faddeev) in the representation theory of noncompact semisimple quantum groups. Explicit formulae for the Whittaker vectors and Whittaker functions are presented in terms of the double sine functions.
A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting
2015
Abstract A Kurzweil-Henstock type integral with respect to an abstract derivation basis in a topological measure space, for Riesz space-valued functions, is studied. A Hake-type theorem is proved for this integral, by using technical properties of Riesz spaces.
Artin groups of spherical type up to isomorphism
2003
AbstractWe prove that two Artin groups of spherical type are isomorphic if and only if their defining Coxeter graphs are the same.
Non linear representations of Lie Groups
1977
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