222,730 research outputs found
W, Linear and Non-local \W-Algebras in Sp(4) Particle Model
We comment on relations between the linear W_{2,4}^{linear} algebra and
non-linear W(2,4)$ algebra appearing in a Sp(4) particle mechanics model by
using Lax equations. The appearance of the non-local V_{2,2} algebra is also
studied.Comment: 10 pages, late
Rooted tree maps and the derivation relation for multiple zeta values
Rooted tree maps assign to an element of the Connes-Kreimer Hopf algebra of
rooted trees a linear map on the noncommutative polynomial algebra in two
letters. Evaluated at any admissible word these maps induce linear relations
between multiple zeta values. In this note we show that the derivation
relations for multiple zeta values are contained in this class of linear
relations.Comment: 6 page
sl(N) Onsager's Algebra and Integrability
We define an analog of Onsager's Algebra through a finite set of
relations that generalize the Dolan Grady defining relations for the original
Onsager's Algebra. This infinite-dimensional Lie Algebra is shown to be
isomorphic to a fixed point subalgebra of Loop Algebra with respect
to a certain involution. As the consequence of the generalized Dolan Grady
relations a Hamiltonian linear in the generators of Onsager's Algebra
is shown to posses an infinite number of mutually commuting integrals of
motion
Non-linear generalization of the sl(2) algebra
We present a generalization of the sl(2) algebra where the algebraic
relations are constructed with the help of a general function of one of the
generators. When this function is linear this algebra is a deformed sl(2)
algebra. In the non-linear case, the finite dimensional representations are
constructed in two different ways. In the first case, which provides finite
dimensional representations only for the non-linear case, these representations
come from solutions to a dynamical equation and we show how to construct
explicitly these representations for a general quadratic non-linear function.
The other type of finite dimensional representation comes from solutions to a
cut condition equation. We give examples of solutions of this type in the
non-linear case as well.Comment: 13 pages, 3 EPS figures, Late
- …