Results 11 to 20 of about 111,398 (133)
Hochschild cohomology of group extensions of quantum symmetric algebras [PDF]
, 2010 Quantum symmetric algebras (or noncommutative polynomial rings) arise in many places in mathematics. In this article we find the multiplicative structure of their Hochschild cohomology when the coefficients are in an arbitrary bimodule algebra. When this
Communicated Martin Lorenz +3 more
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The Eight Dimensional Quantum Hall Effect and the Octonions
, 2003 We construct a generalization of the quantum Hall effect where particles move in an eight dimensional space under an SO(8) gauge field. The underlying mathematics of this particle liquid is that of the last normed division algebra, the octonions.
B. Grossman +5 more
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Free Rota-Baxter algebras and rooted trees
, 2008 A Rota-Baxter algebra, also known as a Baxter algebra, is an algebra with a linear operator satisfying a relation, called the Rota-Baxter relation, that generalizes the integration by parts formula.
Aguiar M. +18 more
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Non-commutative fermion mass matrix and gravity
, 2013 The first part is an introductory description of a small cross-section of the literature on algebraic methods in non-perturbative quantum gravity with a specific focus on viewing algebra as a laboratory in which to deepen understanding of the nature of ...
Baez J. C. +12 more
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Hypercomplex Algebras and their application to the mathematical formulation of Quantum Theory
, 2014 Quantum theory (QT), namely in terms of Schr dinger's 1926 wave functions in general requires complex numbers to be formulated. However, it soon turned out to even require some hypercomplex algebra. Incorporating Special Relativity leads to an equation (Dirac 1928) requiring pairwise anti-commuting coefficients, usually $4\times 4$ matrices. A unitary
Hertig, Torsten +2 more
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On the Cyclotomic Quantum Algebra of Time Perception [PDF]
, 2004 I develop the idea that time perception is the quantum counterpart to time measurement. Phase-locking and prime number theory were proposed as the unifying concepts for understanding the optimal synchronization of clocks and their 1/f frequency noise ...
Planat, Michel
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The irreducible modules for the derivations of the rational quantum torus
, 2014 Let $\bbcq$ be the quantum torus associated with the $d \times d$ matrix $q = (q_{ij})$, $q_{ii} = 1$, $q_{ij}^{-1} = q_{ji}$, $q_{ij}$ are roots of unity, for all $1 \leq i, j \leq d.$ Let $\Der(\bbcq)$ be the Lie algebra of all the derivations of ...
Batra, Punita +2 more
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Yang-Baxter Equations, Computational Methods and Applications
, 2015 Computational methods are an important tool for solving the Yang-Baxter equations(in small dimensions), for classifying (unifying) structures, and for solving related problems.
Nichita, Florin F.
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Quantum gravity observables: observation, algebras, and mathematical structure*
Journal of Physics A: Mathematical and TheoreticalAbstract The questions of describing observables and observation in quantum gravity appear to be centrally important to its physics. A relational approach holds significant promise, and a classification of different types of relational observables (gravitationally dressed, field relational, and more general) is outlined.
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World Journal of Neuroscience, 2013 The thesis of this paper is that Information, Cognition and a Principle of Existence are intrinsically structured in the quantum model of reality. We reach such evidence by using the Clifford algebra. We analyze quantization in some traditional cases of quantum mechanics and, in particular in quantum harmonic oscillator, orbital angular momentum ...
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