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Waring problem for triangular matrix algebra [PDF]
Linear Algebra and its Applications, 2023 The Matrix Waring problem is if we can write every matrix as a sum of $k$-th powers. Here, we look at the same problem for triangular matrix algebra $T_n(\mathbb{F}_q)$ consisting of upper triangular matrices over a finite field. We prove that for all integers $k, n \geq 1$, there exists a constant $\mathcal C(k, n)$, such that for all $q> \mathcal ...
Rahul Kaushik, Anupam Singh
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Generalized Lie n-derivations on arbitrary triangular algebras
Open Mathematics, 2023 In this study, we consider generalized Lie nn-derivations of an arbitrary triangular algebra TT through the constructed triangular algebra T0{T}_{0}, where T0{T}_{0} is constructed using the notion of maximal left (right) ring of quotients.
Yuan He, Liu Zhuo
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The Characterization of Generalized Jordan Centralizers on Triangular Algebras [PDF]
Journal of Function Spaces, 2018 In this paper, it is shown that if T=Tri(A,M,B) is a triangular algebra and ϕ is an additive operator on T such that (m+n+k+l)ϕ(T2)-(mϕ(T)T+nTϕ(T)+kϕ(I)T2+lT2ϕ(I))∈FI for any T∈T, then ϕ is a centralizer. It follows that an (m,n)- Jordan centralizer on a
Quanyuan Chen +2 more
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Joint and Generalized Spectral Radius of Upper Triangular Matrices with Entries in a Unital Banach Algebra [PDF]
Sahand Communications in Mathematical Analysis, 2020 In this paper, we discuss some properties of joint spectral {radius(jsr)} and generalized spectral radius(gsr) for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized
Hamideh Mohammadzadehkan +2 more
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Quantum groups, Yang–Baxter maps and quasi-determinants
Nuclear Physics B, 2018 For any quasi-triangular Hopf algebra, there exists the universal R-matrix, which satisfies the Yang–Baxter equation. It is known that the adjoint action of the universal R-matrix on the elements of the tensor square of the algebra constitutes a quantum ...
Zengo Tsuboi
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a Triangular Deformation of the Two-Dimensional POINCARÉ Algebra [PDF]
, 1994 Contracting the h-deformation of SL(2, ℝ), we construct a new deformation of two-dimensional Poincare's algebra, the algebra of functions on its group and its differential structure.
M. Khorrami +3 more
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Transposed Poisson structures on the Lie algebra of upper triangular matrices [PDF]
Portugaliae Mathematica, 2023 We describe transposed Poisson structures on the upper triangular matrix Lie algebra $T_n(F)$, $n>1$, over a field $F$ of characteristic zero. We prove that, for $n>2$, any such structure is either of Poisson type or the orthogonal sum of a fixed non ...
I. Kaygorodov, M. Khrypchenko
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Graded polynomial identities for the Lie algebra of upper triangular matrices of order 3 [PDF]
Communications in Algebra, 2022 We compute the graded polynomial identities and its graded codimension sequence for the elementary gradings of the Lie algebra of upper triangular matrices of order 3.
F. Yasumura
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Essentially Triangular Algebras [PDF]
Proceedings of the American Mathematical Society, 1986 If N \mathcal {N} is a nest, then the set of all bounded linear operators T T such that T P − P T P TP - PTP is compact for all P P in N \mathcal {N} is the essentially triangular algebra associated
Erdos, J. A., Hopenwasser, A.
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A Class of Nonlinear Nonglobal Semi-Jordan Triple Derivable Mappings on Triangular Algebras
Journal of Mathematics, 2021 In this paper, we proved that each nonlinear nonglobal semi-Jordan triple derivable mapping on a 2-torsion free triangular algebra is an additive derivation.
Xiuhai Fei, Haifang Zhang
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