— Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different from the original ones. Binary nonlinearization procedure corresponding to the Bargmann symmetry constraint is carried out for those Lax pairs. The proposed Lax pairs together with adjoint Lax pairs are constrained as a hierarchy of commutative, finite dimensional integrable Hamiltonian systems in the Liouville sense,...

Involutivity is the algebraic property that guarantees solutions to an analytic and torsion-free exterior differential system or partial differential equation via the Cartan–Kähler theorem. Guillemin normal form establishes that the prolonged symbol of an involutive system admits a commutativity property on certain subspaces of the prolonged tableau. This article examines Guillemin normal form ...

We show Koszulness of the prop governing involutive Lie bialgebras and also of the props governing non-unital and unital-counital Frobenius algebras, solving a long-standing problem. This gives us minimal models for their deformation complexes, and for deformation complexes of their algebras which are discussed in detail. Using an operad of graph complexes we prove, with the help of an earlier ...

In 1982 Richard P. Stanley conjectured that any finitely generated Zn-graded module M over a finitely generated Nn-graded K-algebra R can be decomposed in a direct sum M = ⊕t i=1 νi Si of finitely many free modules νi Si which have to satisfy some additional conditions. Besides homogeneity conditions the most important restriction is that the Si have to be subalgebras of R of dimension at least...

In 1992 Drinfeld posed the question of finding the set-theoretic solutions of the Yang-Baxter equation. Recently, Gateva-Ivanova and Van den Bergh and Etingof, Schedler and Soloviev have shown a group-theoretical interpretation of involutive non-degenerate solutions. Namely, there is a oneto-one correspondence between involutive non-degenerate solutions on finite sets and groups of I-type. A gr...

The Lax pair of the Ruijsenaars-Schneider model with interaction potential of trigonometric type based on Dn Lie algebra is presented. We give a general form for the Lax pair and prove partial results for small n. Liouville integrability of the corresponding system follows a series of involutive Hamiltonians generated by the characteristic polynomial of the Lax matrix. The rational case appears...

Characterization and new methods of generation of bijective fuzzy negations (involutive, contracting and expanding negations) are done. The approach is based on a symmetry of involutive negations with respect to the line f(x) = x; x∈ [0; 1]. Contracting and expanding negations are given by suitable de4ections from this symmetry. c © 2002 Elsevier B.V. All rights reserved.