Results 21 to 30 of about 8,246 (157)
The geometry of determinant line bundles in noncommutative geometry
Journal of Noncommutative Geometry, 2009 This article is concerned with the study of the geometry of determinant line bundles associated to families of spectral triples parametrized by the moduli space of gauge equivalence classes of Hermitian connections on a Hermitian finite projective module. We illustrate our results with some examples that arise in noncommutative geometry.
Chakraborty, P., Varghese, M.
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Noncommutative determinants, Cauchy–Binet formulae, and Capelli-type identities I. Generalizations of the Capelli and Turnbull identities [PDF]
The Electronic Journal of Combinatorics, 2009 We prove, by simple manipulation of commutators, two noncommutative generalizations of the Cauchy–Binet formula for the determinant of a product. As special cases we obtain elementary proofs of the Capelli identity from classical invariant theory and of Turnbull's Capelli-type identities for symmetric and antisymmetric matrices.
S. Caracciolo +2 more
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Dirac Functional Determinants in Terms of the Eta Invariant and the Noncommutative Residue [PDF]
Communications in Mathematical Physics, 2003 The zeta and eta-functions associated with massless and massive Dirac operators, in a D-dimensional (D odd or even) manifold without boundary, are rigorously constructed. Several mathematical subtleties involved in this process are stressed, as the intrisic ambiguity present in the definition of the associated fermion functional determinant in the ...
Cognola, Guido +2 more
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Noncommutative families of instantons [PDF]
, 2007 We construct $\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\theta$, we construct a noncommutative family of instantons of charge 1.
Landi, Giovanni +3 more
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Noncommutativity Makes Determinants Hard
Information and Computation, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Non-commutative integrability, paths and quasi-determinants
Advances in Mathematics, 2011 In previous work, we showed that the solution of certain systems of discrete integrable equations, notably $Q$ and $T$-systems, is given in terms of partition functions of positively weighted paths, thereby proving the positive Laurent phenomenon of Fomin and Zelevinsky for these cases.
Di Francesco, Philippe, Kedem, Rinat
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A NON-COMMUTATIVE SEMI-DISCRETE TODA EQUATION AND ITS QUASI-DETERMINANT SOLUTIONS [PDF]
Glasgow Mathematical Journal, 2009 AbstractA non-commutative version of the semi-discrete Toda equation is considered. A Lax pair and its Darboux transformations and binary Darboux transformations are found and they are used to construct two families of quasi-determinant solutions.
Li, C.X., Nimmo, J.J.C.
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Quantum gravity: unification of principles and interactions, and promises of spectral geometry [PDF]
, 2007 Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity.
Booss-Bavnbek, Bernhelm +2 more
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New Algorithm and Phase Diagram of Noncommutative Phi**4 on the Fuzzy Sphere [PDF]
, 2014 We propose a new algorithm for simulating noncommutative phi-four theory on the fuzzy sphere based on, i) coupling the scalar field to a U(1) gauge field, in such a way that in the commutative limit N\longrightarrow \infty, the two modes decouple and we ...
Ydri, Badis
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RE-algebras, quasi-determinants and the full Toda system
Partial Differential Equations in Applied MathematicsIn 1991, Gelfand and Retakh embodied the idea of a noncommutative Dieudonne determinant for a generating matrix of RTT algebra, namely, they found a representation of the quantum determinant of RTT algebra in the form of a product of principal quasi ...
Dmitry V. Talalaev
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