13 papers
Ground states on the \(\mathrm{C}^*\)-algebras of Fell bundles over étale groupoids
Md Amir Hossain
Let \(p\colon \mathcal{A}\to G\) be a Fell bundle over a locally compact Hausdorff second countable étale groupoid \(G\) and let \(\mathrm{C}^*(G; \mathcal{A})\) be the associated…
Inclusions of Fell bundles -algebras and coaction crossed products
Md Amir Hossain
Let be a Fell bundle over a locally compact Hausdorff second countable groupoid equipped with a Haar system, and let be a discrete group. Given…
On the Haagerup property for partial crossed products
Md Amir Hossain, Chaitanya J. Kulkarni
Let be a partial dynamical system and let denote the associated reduced partial crossed product. In this article, we introduce the Haagerup property fo…
Some remarks on Reduced -algebras of semigroup dynamical systems and product systems
Md Amir Hossain, S. Sundar
We study the exactness of the reduced crossed product of a semigroup dynamical system and the reduced -algebra of a product system. We show that for a semigroup dynamical sy…
Inductive limits of partial crossed products
Md Amir Hossain
Let be an inductive sequence of partial dynamical systems. We prove the existence of an induced partial action of …
Extreme points of unital completely positive maps invariant under partial action
Chaitanya J. Kulkarni, Md Amir Hossain
The classical Choquet theorem establishes a barycentric decomposition for elements in a compact convex subset of a locally convex topological vector space. This decomposition is ac…
Reduced -algebras of Product Systems -- an -semigroup and a Groupoid perspective
Md Amir Hossain, S. Sundar
For Ore semigroups with an order unit, we prove that there is a bijection between -semigroups over and product systems of -correspondences over . We exp…
Metrics on -algebras of Étale groupoids from length functions
Arnab Chattopadhyay, Md Amir Hossain, Soumalya Joardar
We show that for an étale groupoid with compact unit space, the natural Dirac type operator from a continuous length function produces a natural pseudo-metric on the state space of…
C-algebras of Fell bundles over étale groupoids
Rohit Dilip Holkar, Md Amir Hossain
We describe a construction for the full C-algebra of a possibly unsaturated Fell bundle over a possibly non-Hausdorff locally compact étale groupoid without appealing to Renaul…
KMS states on the -algebras of Fell bundles over {é}tale groupoids
Rohit Dilip Holkar, Md Amir Hossain
Let be a saturated Fell bundle over a locally compact, Hausdorff, second countable, {é}tale groupoid~, and let denote i…
Topological fundamental groupoid. III. Haar systems on the fundamental groupoid
Rohit Dilip Holkar, Md Amir Hossain
Let be a path connected, locally path connected and semilocally simply connected space; let be its universal cover. We discuss the existence and description of a Ha…
Topological Fundamental Groupoid. II. An action category of the fundamental groupoid
Rohit Dilip Holkar, Md Amir Hossain, Dheeraj Kulkarni
For a path connected, locally path connected and semilocally simply connected space , let denote its topologised fundamental groupoid as established in the first articl…
Topological fundamental groupoid. I
Rohit Dilip Holkar, Md Amir Hossain
We show that the fundamental groupoid~\(Π_1(X)\) of a locally path connected semilocally simply connected space~\(X\) can be equipped with a \emph{natural} topology so that it beco…