Cohomological Analysis of Partial
                    Differential Equations and Secondary
                    Calculus

Vinogradov, A. M.

doi:10.1090/mmono/204

Cited by 81 publications

(143 citation statements)

References 0 publications

Supporting

Mentioning

141

Contrasting

Unclassified

Order By: Relevance

“…[1][2][3][4] and also [5][6][7][8][9][10] for reviews. In particular for Lagrangian systems, symmetries of the action, also called variational symmetries, are a subalgebra of the symmetries of the EOM.…”

Section: Classification Of Symmetriesmentioning

confidence: 99%

“…In the non-Lagrangian case, following [45,46,52], we assume that the gauge system is described by a nilpotent, ghost number 1 BRST differential s represented by an evolutionary vector field on a bigraded jet-space of fields, which contains, besides the ghost number, an antifield number 4 Note that, compared to the general case, inequivalent symmetries of linear systems possess a richer structure. Namely, they form an associative algebra with the product induced by the operator product of cohomology representatives.…”

Section: Constraints On Eom Symmetriesmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotically locally flat spacetimes and dynamical nonspherically-symmetric black holes in three dimensions

et al. 2016

View full text Add to dashboard Cite

Section: Classification Of Symmetriesmentioning

confidence: 99%

Section: Constraints On Eom Symmetriesmentioning

confidence: 99%

Asymptotically locally flat spacetimes and dynamical nonspherically-symmetric black holes in three dimensions

et al. 2016

View full text Add to dashboard Cite

“…Definition 2.3 therefore designates a more formal property of diffiety Ω, however, it is in full accordance with quite opposite approach [11], [12], [13], [14], [15], [16] in the theory of exterior differential systems.…”

Section: Definition 23 We Claim That the Solution Of Diffiety ω Depmentioning

confidence: 89%

Report on the Absolute Differential Equations I

Chrastinová¹,

Tryhuk²

2017

AAN

View full text Add to dashboard Cite

The article provides a survey of the absolute theory of general systems of (partial) differential equations. The equations are relieved of all additional structures and subject to quite arbitrary change of the variables. An abstract mathematical theory in the Bourbaki sense with its own concepts and technical tools follows. In particular the external, internal, generalized and higher-order symmetries and infinitesimal symmetries together with the E. Cartan's prolongations, various characteristics, the involutivity and the controllability structures are clarified in genuinely coordinate-free terms without any use of the common jet mechanisms.

show abstract

“…, n). It is also highly interesting to compare diffieties and symmetries [8] with our definitions 2.1-2.3. Remark 3.…”

Section: Lemma 21 a Vector Field Z ∈ T Is A Variation Of Diffiety ωmentioning

confidence: 99%

“…(Roughly saying, the contact forms are preserved after infinitesimal Z-shifts.) The inclusion is equivalent to the congruence 8) this is the infinitesimal version of clumsy formulae (1.4). With this preparation, we can eventually turn to the main topic.…”

Section: Prefacementioning

confidence: 99%

On the internal approach to differential equations 3. Infinitesimal symmetries

Chrastinová

Tryhuk

2016

Mathematica Slovaca

View full text Add to dashboard Cite

Abstract. The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order of derivatives can be changed and the article is devoted to the higher-order infinitesimal symmetries which provide a simplifying "linear aproximation" of general groups of higher-order symmetries. The classical Lie's approach is appropriately adapted. PrefaceIf the invertible higher-order transformations of differential equations are accepted as a reasonable subject, the common Lie-Cartan's methods are insufficient for complete solution of the symmetry problem. We recall that even the structure of all higher-order symmetries of the trivial (empty) systems of differential equations (that is, of the infinite-order jet spaces without any differential constraits) is unknown [1,2,3]. The same can be said for the "linearized theory" of the higher-order infinitesimal transformations treated in this article.Let us outline the core of the subject. We start with surfaceslying in the space R m+n with coordinates x 1 , . . . , x n , w 1 , . . . , w m . The higherorder transformations are defined by formulaē, ··) (i, i ′ = 1, . . . , n; j, j ′ = 1, . . . , m) (1.1)2010 Mathematics Subject Classification. 54A17, 58J99, 35A30.

show abstract

Cohomological Analysis of Partial Differential Equations and Secondary Calculus

Cited by 81 publications

References 0 publications

Asymptotically locally flat spacetimes and dynamical nonspherically-symmetric black holes in three dimensions

Asymptotically locally flat spacetimes and dynamical nonspherically-symmetric black holes in three dimensions

Report on the Absolute Differential Equations I

On the internal approach to differential equations 3. Infinitesimal symmetries

Contact Info

Product

Resources

About