Non-Abelian Lie algebroids over jet spaces

Abstract

We associate Hamiltonian homological evolutionary vector fields --which are the non-Abelian variational Lie algebroids' differentials-- with Lie algebra-valued zero-curvature representations for partial differential equations.

Conf. "Nonlinear Mathematical Physics: 20 Years of JNMP" (Nordfjordeid, Norway, 2013); solution of Problem 12.8 from the book IHES/M-12-13 by the first author. --- Accepted for publication in JNMP (2014), 26 pages (3 figures)

References in corpus (2)

• Variational Poisson-Nijenhuis structures for partial differential equations
• Variational Lie algebroids and homological evolutionary vector fields

Cited by in corpus (4)

• Non-degenerate invariant (super)symmetric bilinear forms on simple Lie (super)algebras
• The calculus of multivectors on noncommutative jet spaces
• The right-hand side of the Jacobi identity: to be naught or not to be?
• On the (non)removability of spectral parameters in $Z_2$-graded zero-curvature representations and its applications