Torsor Theory of Physical Quantities and their Measurement

Domotor, Zoltan

doi:10.1515/msr-2017-0019

Cited by 4 publications

(3 citation statements)

References 8 publications

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“…• Recent works in measurement theory attempt to understand the algebraic structure underlying the quantity calculus using topological bundles (see e.g. [45,46]).…”

Section: Recall That a Continuous Mapmentioning

confidence: 99%

Some interactions between Hopf Galois extensions and noncommutative rings

Calderón

Reyes

2022

Universitas Scientiarum

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In this paper, our objects of interest are Hopf Galois extensions (e.g., Hopf algebras, Galois field extensions, strongly graded algebras, crossed products, principal bundles, etc.) and families of noncommutative rings (e.g., skew polynomial rings, PBW extensions and skew PBW extensions, etc.) We collect and systematize questions, problems, properties and recent advances in both theories by explicitly developing examples and doing calculations that are usually omitted in the literature. In particular, for Hopf Galois extensions we consider approaches from the point of view of quantum torsors (also known as quantum heaps) and Hopf Galois systems, while for some families of noncommutative rings we present advances in the characterization of ring-theoretic and homological properties. Every developed topic is exemplified with abundant references to classic and current works, so this paper serves as a survey for those interested in either of the two theories. Throughout, interactions between both are presented.

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“…• Recent works in measurement theory attempt to understand the algebraic structure underlying the quantity calculus using topological bundles (see e.g. [45,46]).…”

Section: Recall That a Continuous Mapmentioning

confidence: 99%

Some interactions between Hopf Galois extensions and noncommutative rings

Calderón

Reyes

2022

Universitas Scientiarum

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“…• Recent works in measurement theory attempt to understand the algebraic structure underlying the quantity calculus as topological bundles (cf. [37,107]).…”

Section: Comparing We Get Thatmentioning

confidence: 99%

Some interactions between Hopf Galois extensions and noncommutative rings

Calderón,

Reyes

2021

Preprint

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In this memoir, we consider Hopf Galois extensions and families of noncommutative rings known as skew polynomial rings, PBW extensions and skew PBW extensions. We address remarkable examples of Hopf Galois extensions (e.g., Hopf algebras, field extensions, strongly graded algebras, crossed products, principal bundles), some properties and recent advances in the theory such as quantum torsors and Hopf Galois systems. Next, we study the families of noncommutative rings and some of its basic properties and recall remarkable examples appearing in the theory. Finally, some interactions between all families of rings are presented.

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“…and similarly for tensors of other types. Therefore (50) The formulae for the covariant derivative (29), connection coefficients (32), and curvature tensors (39) remain valid for a connection compatible with the metric. In this case the connection coefficients can be obtained from the metric by the formulae 37…”

Section: Metric and Related Tensors And Operationsmentioning

confidence: 99%

Dimensional analysis in relativity and in differential geometry

Mana¹

2021

Eur. J. Phys.

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This note provides a short guide to dimensional analysis in Lorentzian and general relativity and in differential geometry. It tries to revive Dorgelo and Schouten’s notion of ‘intrinsic’ or ‘absolute’ dimension of a tensorial quantity. The intrinsic dimension is independent of the dimensions of the coordinates and expresses the physical and operational meaning of a tensor. The dimensional analysis of several important tensors and tensor operations is summarized. In particular it is shown that the components of a tensor need not have all the same dimension, and that the Riemann (once contravariant and thrice covariant) and Ricci (fully covariant) curvature tensors are dimensionless. The relation between dimension and operational meaning for the metric and stress–energy–momentum tensors is discussed; and the main conventions for the dimensions of these two tensors and of Einstein's constant are reviewed. A more thorough and updated analysis is available as a preprint.

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Torsor Theory of Physical Quantities and their Measurement

Cited by 4 publications

References 8 publications

Some interactions between Hopf Galois extensions and noncommutative rings

Some interactions between Hopf Galois extensions and noncommutative rings

Some interactions between Hopf Galois extensions and noncommutative rings

Dimensional analysis in relativity and in differential geometry

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