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Functional Identities on Matrix Algebras [PDF]
Algebras and Representation Theory, 2015 20 pages, comments welcome, version 2- applications have been ...
Brešar, Matej, Spenko, Špela
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Perturbations of matrix algebras.
Michigan Mathematical Journal, 1986 Two subalgebras of \({\mathcal M}_ n\), the \(n\times n\) matrices, are close if their unit balls are close in the Hausdorff metric. Several examples of pathological behaviour are given. For example, close algebras need not be isomorphic; they may be isomorphic via a map close to the identity but not be similar; and they may be similar and close, but ...
Choi, Man Duen, Davidson, Kenneth R.
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Generalized Matrix Algebras [PDF]
Canadian Journal of Mathematics, 1955 The algebras considered here arose in the investigation of an algebra connected with the orthogonal group. We consider an algebra of dimension mn over a field K of characteristic zero, and possessing a basis {eij} (1 ≤ i ≤ m; 1 ≤ j ≤ n) with the multiplication property1,The field elements ϕij form a matrix Φ = (ϕij) of order n × m.
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Journal of Algebra, 1998 Let \(M\) be an invertible \(r\times r\) matrix with integer coefficients and identify it with the linear mapping \(Z^r\to Z^r\) induced by it. Two integer matrices \(A,B\) are called equivalent, if \(\det(AB^{-1})=\pm 1\). Denote by \(LD(M)\) the set of equivalence classes of left divisors of \(M\) ordered by divisibility, and let \(G(M)\) be the ...
Bhowmik, Gautami, Ramaré, Olivier
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On the Symmetry of Matrix Algebras [PDF]
Proceedings of the American Mathematical Society, 1976 A ∗
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Stratifying algebras with near-matrix algebras
Journal of Pure and Applied Algebra, 2004 For a left module \(U\) and a right module \(V\) over an algebra \(D\) with a \(D\)-\(D\) bilinear form \(\beta\colon U\times V\to D\), an associative algebra structure can be defined on the tensor product \(V\otimes_DU\) which is called a near matrix algebra.
Du, Jie, Lin, Zongzhu
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The Cartan matrix of a centralizer algebra
Proceedings - Mathematical Sciences, 2012 The centralizer algebra of a matrix consists of those matrices that commute with it. We investigate the basic representation-theoretic invariants of centralizer algebras, namely their radicals, projective indecomposable modules, injective indecomposable modules, simple modules and Cartan matrices.
Dubey, Umesh V. +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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On Amenability-Like Properties of a Class of Matrix Algebras
Journal of Mathematics, 2022 In this study, we show that a matrix algebra ℒℳIpA is a dual Banach algebra, where A is a dual Banach algebra and 1≤p≤2. We show that ℒℳIpℂ is Connes amenable if and only if I is finite, for every nonempty set I.
M. Rostami, S. F. Shariati, A. Sahami
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Frobenius structural matrix algebras
Linear Algebra and its Applications, 2013 We discuss when the incidence coalgebra of a locally finite preordered set is right co-Frobenius. As a consequence, we obtain that a structural matrix algebra over a field $k$ is Frobenius if and only if it consists, up to a permutation of rows and columns, of diagonal blocks which are full matrix algebras over $k$.
Dăscălescu, S. +2 more
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