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𝒟 -bundles and integrable hierarchies

David Ben-Zvi, Thomas Nevins (2011)

Journal of the European Mathematical Society

We study the geometry of 𝒟 -bundles—locally projective 𝒟 -modules—on algebraic curves, and apply them to the study of integrable hierarchies, specifically the multicomponent Kadomtsev–Petviashvili (KP) and spin Calogero–Moser (CM) hierarchies. We show that KP hierarchies have a geometric description as flows on moduli spaces of 𝒟 -bundles; in particular, we prove that the local structure of 𝒟 -bundles is captured by the full Sato Grassmannian. The rational, trigonometric, and elliptic solutions of KP...

ℤ -graded Lie superalgebras of infinite depth and finite growth

Nicoletta Cantarini (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In 1998 Victor Kac classified infinite-dimensional ℤ -graded Lie superalgebras of finite depth. We construct new examples of infinite-dimensional Lie superalgebras with a ℤ -gradation of infinite depth and finite growth and classify ℤ -graded Lie superalgebras of infinite depth and finite growth under suitable hypotheses.

A special type of triangulations in numerical nonlinear analysis.

J. M. Soriano (1990)

Collectanea Mathematica

To calculate the zeros of a map f : Rn → Rn we consider the class of triangulations of Rn so that a certain point belongs to a simplex of fixed diameter and dimension. In this paper two types of this new class of triangulations are constructed and shown to be useful to calculate zeros of piecewise linear approximations of f.

Almost-graded central extensions of Lax operator algebras

Martin Schlichenmaier (2011)

Banach Center Publications

Lax operator algebras constitute a new class of infinite dimensional Lie algebras of geometric origin. More precisely, they are algebras of matrices whose entries are meromorphic functions on a compact Riemann surface. They generalize classical current algebras and current algebras of Krichever-Novikov type. Lax operators for 𝔤𝔩(n), with the spectral parameter on a Riemann surface, were introduced by Krichever. In joint works of Krichever and Sheinman their algebraic structure was revealed and...

Banach manifolds of algebraic elements in the algebra ℒ (H) of bounded linear operatorsof bounded linear operators

José Isidro (2005)

Open Mathematics

Given a complex Hilbert space H, we study the manifold 𝒜 of algebraic elements in Z = ℒ H . We represent 𝒜 as a disjoint union of closed connected subsets M of Z each of which is an orbit under the action of G, the group of all C*-algebra automorphisms of Z. Those orbits M consisting of hermitian algebraic elements with a fixed finite rank r, (0< r<∞) are real-analytic direct submanifolds of Z. Using the C*-algebra structure of Z, a Banach-manifold structure and a G-invariant torsionfree affine...

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