scholarly journals Hamiltonian operators in differential algebras

2017 ◽  
Vol 193 (3) ◽  
pp. 1725-1736 ◽  
Author(s):  
V. V. Zharinov
Keyword(s):  
Differential Algebras ◽  
Hamiltonian Operators

On A Multiplicativity up to Homotopy of the Gugenheim Map

2002 ◽  
Vol 9 (3) ◽  
pp. 549-566
Author(s):  
Z. Kharebava
Keyword(s):  
Cochain Complex ◽  
Differential Algebras ◽  
Graded Coalgebra

Abstract In the category of differential algebras with strong homotopy there is a Gugenheim's map {ρ 𝑖} : 𝐴* → 𝐶* from Sullivan's commutative cochain complex to the singular cochain complex of a space, which induces a differential graded coalgebra map of appropriate Bar constructions. Both (𝐵𝐴*, dBA , Δ,) and (𝐵𝐶*, dBC* , Δ,) carry multiplications. We show that the Gugenheim's map 𝐵{ρ 𝑖} : (𝐵𝐴*, dBA* , Δ,) → (𝐵𝐶*, dBC* , Δ,) is multiplicative up to homotopy with respect to these structures.

scholarly journals On integro-differential algebras

2014 ◽  
Vol 218 (3) ◽  
pp. 456-473 ◽  
Author(s):  
Li Guo ◽  
Georg Regensburger ◽  
Markus Rosenkranz
Keyword(s):  
Differential Algebras

scholarly journals Optimal embeddings of ultradistributions into differential algebras

2017 ◽  
Vol 186 (3) ◽  
pp. 407-438 ◽  
Author(s):  
Andreas Debrouwere ◽  
Hans Vernaeve ◽  
Jasson Vindas
Keyword(s):  
Differential Algebras

scholarly journals Reduced Pre-Lie Algebraic Structures, the Weak and Weakly Deformed Balinsky–Novikov Type Symmetry Algebras and Related Hamiltonian Operators

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 601
Author(s):  
Orest Artemovych ◽  
Alexander Balinsky ◽  
Denis Blackmore ◽  
Anatolij Prykarpatski
Keyword(s):  
Dynamical Systems ◽  
Lie Algebras ◽  
Algebraic Structures ◽  
Loop Algebras ◽  
Type Symmetry ◽  
Novikov Algebras ◽  
Algebra Theory ◽  
Hamiltonian Operators ◽  
Adjoint Space ◽  
Algebraic Scheme

The Lie algebraic scheme for constructing Hamiltonian operators is differential-algebraically recast and an effective approach is devised for classifying the underlying algebraic structures of integrable Hamiltonian systems. Lie–Poisson analysis on the adjoint space to toroidal loop Lie algebras is employed to construct new reduced pre-Lie algebraic structures in which the corresponding Hamiltonian operators exist and generate integrable dynamical systems. It is also shown that the Balinsky–Novikov type algebraic structures, obtained as a Hamiltonicity condition, are derivations on the Lie algebras naturally associated with differential toroidal loop algebras. We study nonassociative and noncommutive algebras and the related Lie-algebraic symmetry structures on the multidimensional torus, generating via the Adler–Kostant–Symes scheme multi-component and multi-dimensional Hamiltonian operators. In the case of multidimensional torus, we have constructed a new weak Balinsky–Novikov type algebra, which is instrumental for describing integrable multidimensional and multicomponent heavenly type equations. We have also studied the current algebra symmetry structures, related with a new weakly deformed Balinsky–Novikov type algebra on the axis, which is instrumental for describing integrable multicomponent dynamical systems on functional manifolds. Moreover, using the non-associative and associative left-symmetric pre-Lie algebra theory of Zelmanov, we also explicate Balinsky–Novikov algebras, including their fermionic version and related multiplicative and Lie structures.

THE THEORY OF FREE DIFFERENTIAL ALGEBRAS AND SOME APPLICATIONS

1991 ◽  
pp. 794-831
Author(s):  
Leonardo Castellani ◽  
Riccardo D’ Auria ◽  
Pietro Fré
Keyword(s):  
Differential Algebras
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