9 citations · 26 across the 6 of their papers we have counts for
7 papers
A 2X2 Matrix Approach to Hopf Fibrations:: Quaternionic Reduction of Octonionic Bi-unitary Matrices and an RLLR/LRRL Bracketing Rule
Jean-Pierre Gazeau, Aneta Sliżewska
We develop a common two-by-two matrix framework for the four classical Hopf fibrations associated with the real, complex, quaternionic and octonionic numbers. In all four cases the…
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…
Symmetries of the space of connections on a principal G-bundle and related symplectic structures
Grzegorz Jakimowicz, Anatol Odzijewicz, Aneta Sliżewska
We investigate G-invariant symplectic structures on the cotangent bundle T*P of a principal G-bundle P(M,G) which are canonically related to automorphisms of the tangent bundle TP…
Fibre-wise linear Poisson structures related to W*-algebras
Anatol Odzijewicz, Grzegorz Jakimowicz, Aneta Sliżewska
In this paper we investigate fiber-wise linear complex Banach sub-Poisson structures defined canonically by the structure of a W*-algebra M. In particular we show that these struct…
Poisson Geometry Related to Atiyah Sequences
Kirill Mackenzie, Anatol Odzijewicz, Aneta Sliżewska
We construct and investigate a short exact sequence of Poisson -groupoids which is canonically related to the Atiyah sequence of a -principal bundle . Our resul…
Algebroids associated to the groupoid of partially invertible elements of a -algebra
Anatol Odzijewicz, Grzegorz Jakimowicz, Aneta Sliżewska
In the paper we study the algebroid A of the groupoid of partially invertible elements over the lattice of orthogonal projections of a -algebra. In particular the complex anal…
Groupoids and inverse semigroups associated to W*-algebras
Anatol Odzijewicz, Aneta Sliżewska
We investigate the Banach Lie groupoids and inverse semigroups naturally associated to W*-algebras. We also present statements describing relationship between these groupoids and t…