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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 PseudoDifferential Operators
Letters in Mathematical Physics, 2002CoAuthors: Carina Boyallian, Jose I. LiberatiAbstract:We classify all the quasifinite highestweight modules over the central extension of the Lie Algebra of Matrix quantum pseudodifferential 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, 2001CoAuthors: Carina Boyallian, Jose I. LiberatiAbstract:We give a complete description of the antiinvolutions of the Algebra DN of N×NMatrix 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) (orthosymplectic). 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, 1998CoAuthors: 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 nonzero diagonals over the AlgebraR m =ℂ[t]/(tm+1). The unitary ones are classified as well. Similar results are obtained for the sinAlgebras.
Carina Boyallian – 2nd expert on this subject based on the ideXlab platform

Lie subAlgebras of the Matrix quantum pseudo differential operators
arXiv: Mathematical Physics, 2016CoAuthors: Karina Batistelli, Carina BoyallianAbstract:We give a complete description of the antiinvolutions 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, 2016CoAuthors: Karina Batistelli, Carina BoyallianAbstract:We give a complete description of the antiinvolutions that preserve the principal gradation of the Algebra of Matrix quantum pseudodifferential operators and we describe the Lie subAlgebras of their minus fixed points.

Quasifinite highest weight modules over WN∞
Journal of Physics A, 2011CoAuthors: Carina Boyallian, Vanesa MeinardiAbstract:In this paper, we classify the irreducible quasifinite 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 Algebra of Matrix finite bounded operators
Journal of Mathematical Analysis and Applications, 2019CoAuthors: 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 nonzero 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 Matrixfinite bounded operators
Journal of Mathematical Analysis and Applications, 2019CoAuthors: 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 nonzero 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, 2018CoAuthors: 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 $k$ nonzero 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.