16 citations · 31 across the 11 of their papers we have counts for
11 papers
Poisson structure on predual of Banach Lie algebroid
Tomasz Goliński, Grzegorz Jakimowicz
We construct the linear Poisson bracket on the predual bundle of a Banach Lie algebroid. It is an alternative approach to the already known results on the linear sub-Poisson struct…
Poisson structures in the Banach setting: comparison of different approaches
Tomasz Goliński, Praful Rahangdale, Alice Barbora Tumpach
In this paper we examine various approaches to the notion of Poisson manifold in the context of Banach manifolds. Existing definitions are presented and differences between them ar…
Nijenhuis operators on homogeneous spaces related to -algebras
Tomasz Goliński, Gabriel Larotonda, Alice Barbora Tumpach
For a unital non-simple -algebra we consider its Banach--Lie group of invertible elements. For a given closed ideal in , we consider…
Nijenhuis operators on Banach homogeneous spaces
Tomasz Goliński, Gabriel Larotonda, Alice Barbora Tumpach
For a Banach--Lie group and an embedded Lie subgroup we consider the homogeneous Banach manifold . In this context we establish the most general conditions…
Geometry of Integrable Systems Related to the Restricted Grassmannian
Tomasz Goliński, Alice Barbara Tumpach
A hierarchy of differential equations on a Banach Lie-Poisson space related to the restricted Grassmannian is studied. Flows on the groupoid of partial isometries and on the restri…
Banach Lie groupoid of partial isometries over restricted Grassmannian
Tomasz Goliński, Grzegorz Jakimowicz, Aneta Sliżewska
The set of partial isometries in a W*-algebra possesses a structure of Banach Lie groupoid. In this paper the differential structure on the set of partial isometries over the restr…
Integrable system on partial isometries: a finite dimensional picture
Tomasz Goliński, Alice Barbora Tumpach
The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit soluti…
Regulated curves on a Banach manifold and singularities of endpoint map. I. Banach manifold structure
Tomasz Goliński, Fernand Pelletier
We consider regulated curves in a Banach bundle whose projection on the basis is continuous with regulated derivative. We build a Banach manifold structure on the set of such curve…
Banach-Lie groupoids and generalized inversion
Daniel Beltiţă, Tomasz Goliński, Grzegorz Jakimowicz +1
We study a few basic properties of Banach-Lie groupoids and algebroids, adapting some classical results on finite dimensional Lie groupoids. As an illustration of the general theor…
Queer Poisson brackets
Daniel Beltita, Tomasz Goliński, Alice-Barbara Tumpach
We give a method to construct Poisson brackets on Banach manifolds~, for which the value of at some point may depend on higher order derivat…
Lie bundle on the space of deformed skew-symmetric matrices
Alina Dobrogowska, Tomasz Goliński
We study a Lie algebra of deformed skew-symmetric matrices endowed with a Lie bracket given by a choice of deformed symmetric matrix.…