The Experts below are selected from a list of 66 Experts worldwide ranked by ideXlab platform
Jose I. Liberati - One of the best experts on this subject based on the ideXlab platform.
-
On Modules over Matrix Quantum Pseudo-Differential Operators
Letters in Mathematical Physics, 2002Co-Authors: Carina Boyallian, Jose I. LiberatiAbstract:We classify all the quasifinite highest-weight modules over the central extension of the Lie Algebra of Matrix quantum pseudo-differential operators, and obtain them in terms of representation theory of the Lie Algebra $$\widehat{{\text{gl}}}$$ (∞, R _ m ) of infinite matrices with only finitely many nonzero diagonals over the Algebra R _ m = $$\mathbb{C}$$ [ t ]/( t ^ m +1). We also classify the unitary ones.
-
Classical Lie subAlgebras of the Lie Algebra of Matrix differential operators on the circle
Journal of Mathematical Physics, 2001Co-Authors: Carina Boyallian, Jose I. LiberatiAbstract:We give a complete description of the anti-involutions of the Algebra DN of N×N-Matrix differential operators on the circle, preserving the principal Z gradation. We obtain, up to conjugation, two families σ±,m with 1⩽m⩽N, getting two families D±,mN of simple Lie subAlgebras fixed by −σ±,m. We also give a geometric realization of σ±,m, concluding that D+,mN is a subAlgebra of DN of type o(m,n) and D−,mN is a subAlgebra of DN of type osp(m,n) (ortho-symplectic). Finally, we study the conformal Algebras associated with D+,mN and D−,mN.
-
quasifinite highest weight modules over the lie Algebra of Matrix differential operators on the circle
Journal of Mathematical Physics, 1998Co-Authors: Carina Boyallian, Jose I. LiberatiAbstract:We classify positive energy representations with finite degeneracies of the Lie AlgebraW1+∞ and construct them in terms of representation theory of the Lie Algebra\(\hat gl(\infty ,R_m )\) of infinites matrices with finite number of non-zero diagonals over the AlgebraR m =ℂ[t]/(tm+1). The unitary ones are classified as well. Similar results are obtained for the sin-Algebras.
Carina Boyallian - One of the best experts on this subject based on the ideXlab platform.
-
Lie subAlgebras of the Matrix quantum pseudo differential operators
arXiv: Mathematical Physics, 2016Co-Authors: Karina Batistelli, Carina BoyallianAbstract:We give a complete description of the anti-involutions that preserve the principal gradation of the Algebra of Matrix quantum pseudodifferential operators and we describe the Lie subAlgebras of its minus fixed points.
-
Lie SubAlgebras of the Matrix Quantum Pseudodifferential Operators
Advances in Mathematical Physics, 2016Co-Authors: Karina Batistelli, Carina BoyallianAbstract:We give a complete description of the anti-involutions that preserve the principal gradation of the Algebra of Matrix quantum pseudodifferential operators and we describe the Lie subAlgebras of their minus fixed points.
-
Quasi-finite highest weight modules over WN∞
Journal of Physics A, 2011Co-Authors: Carina Boyallian, Vanesa MeinardiAbstract:In this paper, we classify the irreducible quasi-finite highest weight modules of the Lie subAlgebras WN∞, p of the Lie Algebra of Matrix differential operators on the circle. We also realize the WN∞-modules in terms of the representation theory of the complex Lie Algebra gl[m]∞ of infinite matrices with a finite number of nonzero diagonals with entries in the Algebra of truncated polynomials.
-
QHWM of the orthogonal type Lie subAlgebra of the Lie Algebra of Matrix differential operators on the circle
Journal of Mathematical Physics, 2010Co-Authors: Carina Boyallian, Vanesa MeinardiAbstract:In this paper we classify the irreducible quasifinite highest weight modules of the orthogonal Lie subAlgebra of the Lie Algebra of Matrix differential operators on the circle. We also realize them in terms of the representation theory of the complex Lie Algebra gl∞[m] of infinite matrices with a finite number of nonzero diagonals with entries in the Algebra of truncated polynomials and the corresponding subAlgebras of type B and D.
-
On Modules over Matrix Quantum Pseudo-Differential Operators
Letters in Mathematical Physics, 2002Co-Authors: Carina Boyallian, Jose I. LiberatiAbstract:We classify all the quasifinite highest-weight modules over the central extension of the Lie Algebra of Matrix quantum pseudo-differential operators, and obtain them in terms of representation theory of the Lie Algebra $$\widehat{{\text{gl}}}$$ (∞, R _ m ) of infinite matrices with only finitely many nonzero diagonals over the Algebra R _ m = $$\mathbb{C}$$ [ t ]/( t ^ m +1). We also classify the unitary ones.
Vladimir Manuilov - One of the best experts on this subject based on the ideXlab platform.
-
on the c Algebra of Matrix finite bounded operators
Journal of Mathematical Analysis and Applications, 2019Co-Authors: Vladimir ManuilovAbstract:Abstract Let H be a separable Hilbert space with a fixed orthonormal basis. Let B ( k ) ( H ) denote the set of operators, whose matrices have no more than k non-zero entries in each line and in each column. The closure of the union (over k ∈ N ) of B ( k ) ( H ) is a C ⁎ -Algebra. We study some properties of this C ⁎ -Algebra. We show that this C ⁎ -Algebra is not an A W ⁎ -Algebra, its group of invertibles is contractible. and it gives rise to an example of a C ⁎ -Algebra with a dense ⁎-subAlgebra and a maximal closed ideal with zero intersection.
-
On the C⁎-Algebra of Matrix-finite bounded operators
Journal of Mathematical Analysis and Applications, 2019Co-Authors: Vladimir ManuilovAbstract:Abstract Let H be a separable Hilbert space with a fixed orthonormal basis. Let B ( k ) ( H ) denote the set of operators, whose matrices have no more than k non-zero entries in each line and in each column. The closure of the union (over k ∈ N ) of B ( k ) ( H ) is a C ⁎ -Algebra. We study some properties of this C ⁎ -Algebra. We show that this C ⁎ -Algebra is not an A W ⁎ -Algebra, its group of invertibles is contractible. and it gives rise to an example of a C ⁎ -Algebra with a dense ⁎-subAlgebra and a maximal closed ideal with zero intersection.
-
on the c Algebra of Matrix finite bounded operators
arXiv: Operator Algebras, 2018Co-Authors: Vladimir ManuilovAbstract:Let $H$ be a separable Hilbert space with a fixed orthonormal basis. Let $\mathbb B^{(k)}(H)$ denote the set of operators, whose matrices have no more than $k$ non-zero entries in each line and in each column. The closure of the union (over $k\in\mathbb N$) of $\mathbb B^{(k)}(H)$ is a C*-Algebra. We study some properties of this C*-Algebra. We show that this C*-Algebra is not an AW*-Algebra, has a proper closed ideal greater than compact operators, and its group of invertibles is contractible.
Vanesa Meinardi - One of the best experts on this subject based on the ideXlab platform.
-
Quasi-finite highest weight modules over WN∞
Journal of Physics A, 2011Co-Authors: Carina Boyallian, Vanesa MeinardiAbstract:In this paper, we classify the irreducible quasi-finite highest weight modules of the Lie subAlgebras WN∞, p of the Lie Algebra of Matrix differential operators on the circle. We also realize the WN∞-modules in terms of the representation theory of the complex Lie Algebra gl[m]∞ of infinite matrices with a finite number of nonzero diagonals with entries in the Algebra of truncated polynomials.
-
QHWM of the orthogonal type Lie subAlgebra of the Lie Algebra of Matrix differential operators on the circle
Journal of Mathematical Physics, 2010Co-Authors: Carina Boyallian, Vanesa MeinardiAbstract:In this paper we classify the irreducible quasifinite highest weight modules of the orthogonal Lie subAlgebra of the Lie Algebra of Matrix differential operators on the circle. We also realize them in terms of the representation theory of the complex Lie Algebra gl∞[m] of infinite matrices with a finite number of nonzero diagonals with entries in the Algebra of truncated polynomials and the corresponding subAlgebras of type B and D.
Allan I Solomon - One of the best experts on this subject based on the ideXlab platform.
-
a three parameter hopf deformation of the Algebra of feynman like diagrams
Journal of Russian Laser Research, 2010Co-Authors: Gerard Duchamp, Pawel Blasiak, A Horzela, K A Penson, Allan I SolomonAbstract:We construct a three-parameter deformation of the Hopf Algebra LDIAG. This is the Algebra that appears in an expansion in terms of Feynman-like diagrams of the product formula in a simplified version of quantum field theory. This new Algebra is a true Hopf deformation which reduces to LDIAG for some parameter values and to the Algebra of Matrix quasi-symmetric functions (MQSym) for others, and thus relates LDIAG to other Hopf Algebras of contemporary physics. Moreover, there is an onto linear mapping preserving products from our Algebra to the Algebra of Euler–Zagier sums.
-
a three parameter hopf deformation of the Algebra of feynman like diagrams
arXiv: Mathematical Physics, 2007Co-Authors: Gerard Duchamp, Pawel Blasiak, A Horzela, K A Penson, Allan I SolomonAbstract:We construct a three-parameter deformation of the Hopf Algebra $\LDIAG$. This is the Algebra that appears in an expansion in terms of Feynman-like diagrams of the {\em product formula} in a simplified version of Quantum Field Theory. This new Algebra is a true Hopf deformation which reduces to $\LDIAG$ for some parameter values and to the Algebra of Matrix Quasi-Symmetric Functions ($\MQS$) for others, and thus relates $\LDIAG$ to other Hopf Algebras of contemporary physics. Moreover, there is an onto linear mapping preserving products from our Algebra to the Algebra of Euler-Zagier sums.