Algebraic Classification of Field Equations

2012 ◽  
pp. 465-536
Author(s):  
Anadijiban Das ◽  
Andrew DeBenedictis
Keyword(s):  
Field Equations ◽  
Algebraic Classification

scholarly journals The Algebraic and Geometric Classification of Four Dimensional Superalgebras

2021 ◽  
Author(s):  
◽  
Aaron Armour
Keyword(s):  
Classification Problem ◽  
Associative Algebras ◽  
New Variety ◽  
Graded Algebras ◽  
Finite Representation ◽  
Algebraic Classification ◽  
Irreducible Components ◽  
Module Algebras ◽  
Sweedler’S Hopf Algebra

<p><b>The algebraic and geometric classification of k-algbras, of dimension fouror less, was started by Gabriel in “Finite representation type is open” [12].</b></p> <p>Several years later Mazzola continued in this direction with his paper “Thealgebraic and geometric classification of associative algebras of dimensionfive” [21]. The problem we attempt in this thesis, is to extend the resultsof Gabriel to the setting of super (or Z2-graded) algebras — our main effortsbeing devoted to the case of superalgebras of dimension four. Wegive an algebraic classification for superalgebras of dimension four withnon-trivial Z2-grading. By combining these results with Gabriel’s we obtaina complete algebraic classification of four dimensional superalgebras.</p> <p>This completes the classification of four dimensional Yetter-Drinfeld modulealgebras over Sweedler’s Hopf algebra H4 given by Chen and Zhangin “Four dimensional Yetter-Drinfeld module algebras over H4” [9]. Thegeometric classification problem leads us to define a new variety, Salgn —the variety of n-dimensional superalgebras—and study some of its properties.</p> <p>The geometry of Salgn is influenced by the geometry of the varietyAlgn yet it is also more complicated, an important difference being thatSalgn is disconnected. While we make significant progress on the geometricclassification of four dimensional superalgebras, it is not complete. Wediscover twenty irreducible components of Salg4 — however there couldbe up to two further irreducible components.</p>

Aleksey Petrov 1954, algebraic classification of the Weyl tensor

2012 ◽  
pp. 81-108
Author(s):  
Andrzej Krasiński ◽  
George F. R. Ellis ◽  
Malcolm A. H. MacCallum
Keyword(s):  
Weyl Tensor ◽  
Algebraic Classification

scholarly journals The algebraic classification of nilpotent associative commutative algebras

2019 ◽  
Vol 19 (11) ◽  
pp. 2050220 ◽  
Author(s):  
Ivan Kaygorodov ◽  
Isamiddin Rakhimov ◽  
Sh. K. Said Husain
Keyword(s):  
Algebraic Classification ◽  
Commutative Algebras

In this paper, we give a complete algebraic classification of [Formula: see text]-dimensional complex nilpotent associative commutative algebras.

scholarly journals The algebraic classification of nilpotent ℭD-algebras

2020 ◽  
pp. 1-47
Author(s):  
Ivan Kaygorodov ◽  
Mykola Khrypchenko
Keyword(s):  
Algebraic Classification

scholarly journals Algebraic classification of higher dimensional spacetimes

2006 ◽  
Vol 38 (3) ◽  
pp. 445-461 ◽  
Author(s):  
A. Coley ◽  
N. Pelavas
Keyword(s):  
Algebraic Classification ◽  
Higher Dimensional

scholarly journals Metric-Affine Geometries with Spherical Symmetry

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 453 ◽  
Author(s):  
Manuel Hohmann
Keyword(s):  
Spherical Symmetry ◽  
Rotation Group ◽  
Spin Connection ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Comprehensive Overview ◽  
Pure Rotation ◽  
Affine Geometries ◽  
Spherically Symmetric Metric

We provide a comprehensive overview of metric-affine geometries with spherical symmetry, which may be used in order to solve the field equations for generic gravity theories which employ these geometries as their field variables. We discuss the most general class of such geometries, which we display both in the metric-Palatini formulation and in the tetrad/spin connection formulation, and show its characteristic properties: torsion, curvature and nonmetricity. We then use these properties to derive a classification of all possible subclasses of spherically symmetric metric-affine geometries, depending on which of the aforementioned quantities are vanishing or non-vanishing. We discuss both the cases of the pure rotation group SO ( 3 ) , which has been previously studied in the literature, and extend these previous results to the full orthogonal group O ( 3 ) , which also includes reflections. As an example for a potential physical application of the results we present here, we study circular orbits arising from autoparallel motion. Finally, we mention how these results can be extended to cosmological symmetry.

scholarly journals Algebraic classification of diffeomorphisms

1979 ◽  
Vol 31 (2) ◽  
pp. 207-219
Author(s):  
R. E. Stong
Keyword(s):  
Algebraic Classification
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