# Algebra of Matrix

The Experts below are selected from a list of 66 Experts worldwide ranked by ideXlab platform

### Jose I. Liberati – 1st expert on this subject based on the ideXlab platform

• ##### On Modules over Matrix Quantum Pseudo-Differential Operators
Letters in Mathematical Physics, 2002
Co-Authors: Carina Boyallian, Jose I. Liberati

Abstract:

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 AlgebraofMatrix differential operators on the circle
Journal of Mathematical Physics, 2001
Co-Authors: Carina Boyallian, Jose I. Liberati

Abstract:

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 AlgebraofMatrix differential operators on the circle
Journal of Mathematical Physics, 1998
Co-Authors: Carina Boyallian, Jose I. Liberati

Abstract:

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 – 2nd expert on this subject based on the ideXlab platform

• ##### Lie subAlgebras of the Matrix quantum pseudo differential operators
arXiv: Mathematical Physics, 2016
Co-Authors: Karina Batistelli, Carina Boyallian

Abstract:

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
Co-Authors: Karina Batistelli, Carina Boyallian

Abstract:

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, 2011
Co-Authors: Carina Boyallian, Vanesa Meinardi

Abstract:

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.

### Vladimir Manuilov – 3rd expert on this subject based on the ideXlab platform

• ##### on the c AlgebraofMatrix finite bounded operators
Journal of Mathematical Analysis and Applications, 2019

Abstract:

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⁎-AlgebraofMatrix-finite bounded operators
Journal of Mathematical Analysis and Applications, 2019
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.