The Polarization Theorem and Polynomial Identities for Matrix Functions
Известия Иркутского государственного университета: Серия "Математика", 2017 In this article the simple combinatorial proof of the known polarization theorem (about the restoration of a polyadditive symmetric function over its values on a diagonal) is given.
G.P. Egorychev
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Applications of the Fuglede-Kadison determinant: Szegö’s theorem and outers for noncommutative $H^p$ [PDF]
Transactions of the American Mathematical Society, 2008 We first use properties of the Fuglede-Kadison determinant on $L^p(M)$, for a finite von Neumann algebra $M$, to give several useful variants of the noncommutative Szeg theorem for $L^p(M)$, including the one usually attributed to Kolmogorov and Krein.
Blecher, David P., Labuschagne, Louis E.
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Some special types of determinants in graded skew P BW extensions.
Revista Integración, 2021 In this paper, we prove that the Nakayama automorphism of a graded skew PBW extension over a finitely presented Koszul Auslanderregular algebra has trivial homological determinant.
Héctor Suárez +2 more
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Cramer’s rules for the system of quaternion matrix equations with η-Hermicity
4 open, 2019 The system of two-sided quaternion matrix equations with η-Hermicity, A1XA1η* = C1 A 1 X A 1 η * = C 1 $ {\mathbf{A}}_1\mathbf{X}{\mathbf{A}}_1^{\eta \mathrm{*}}={\mathbf{C}}_1$ , A2XA2η* = C2 A 2 X A 2 η ...
Kyrchei Ivan I.
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Innerness of derivations into noncommutative symmetric spaces is determined commutatively
, 2023 Let $E=E(0,\infty)$ be a symmetric function space and $E(\mathcal{M},τ)$ be a symmetric operator space associated with a semifinite von Neumann algebra with a faithful normal semifinite trace. Our main result identifies the class of spaces $E$ for which every derivation $δ:\mathcal{A}\to E(\mathcal{M},τ)$ is necessarily inner for each $C^*$-subalgebra $
Huang, Jinghao, Sukochev, Fedor
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THE NONCOMMUTATIVE A-IDEAL OF A (2, 2p + 1)-TORUS KNOT DETERMINES ITS JONES POLYNOMIAL [PDF]
Journal of Knot Theory and Its Ramifications, 2003 The noncommutative A-ideal of a knot is a generalization of the A-polynomial, defined using Kauffman bracket skein modules. In this paper we show that any knot that has the same noncommutative A-ideal as the (2,2p + 1)-torus knot has the same colored Jones polynomials.
Gelca, Răzvan, Sain, Jeremy
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Factorizations of Elements in Noncommutative Rings: A Survey [PDF]
, 2016 We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations.
A Geroldinger +56 more
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Quantum noncommutative gravity in two dimensions [PDF]
, 2005 We study quantisation of noncommutative gravity theories in two dimensions (with noncommutativity defined by the Moyal star product). We show that in the case of noncommutative Jackiw-Teitelboim gravity the path integral over gravitational degrees of ...
Andrianov +48 more
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Noncommutative determinants, Cauchy–Binet formulae, and Capelli-type identities II. Grassmann and quantum oscillator algebra representation [PDF]
Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions, 2014 We prove that, for X , Y , A and B matrices with entries in a non-commutative ring such that
S. Caracciolo, A. Sportiello
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Curvature in Noncommutative Geometry
, 2020 Our understanding of the notion of curvature in a noncommutative setting has progressed substantially in the past ten years. This new episode in noncommutative geometry started when a Gauss-Bonnet theorem was proved by Connes and Tretkoff for a curved ...
A Buium +32 more
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