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Graded Rings and Graded Grothendieck Groups

- R. Hazrat
- Mathematics
- 20 May 2014

Introduction 1. Graded rings and graded modules 2. Graded Morita theory 3. Graded Grothendieck groups 4. Graded Picard groups 5. Classification of graded ultramatricial algebras 6. Graded versus… Expand

Mathematica: A Problem-Centered Approach

- R. Hazrat
- Computer Science
- 13 July 2010

TLDR

The graded Grothendieck group and the classification of Leavitt path algebras

- R. Hazrat
- Mathematics
- 20 February 2011

This paper is an attempt to show that, parallel to Elliott’s classification of AF C*-algebras by means of K-theory, the graded K0-group classifies Leavitt path algebras completely. In this direction,… Expand

Dimension theory and nonstable K1 of quadratic modules

- R. Hazrat
- Mathematics
- 1 December 2002

Employing Bak’s dimension theory, we investigate the nonstable quadratic K-group K1,2n(A, ) = G2n(A, )/E2n(A, ), n 3, where G2n(A, ) denotes the general quadratic group of rank n over a form ring (A,… Expand

Graded Steinberg algebras and their representations

- P. Ara, R. Hazrat, Huanhuan Li, A. Sims
- Mathematics
- 4 April 2017

We study the category of left unital graded modules over the Steinberg algebra of a graded ample Hausdorff groupoid. In the first part of the paper, we show that this category is isomorphic to the… Expand

Reconstruction of graded groupoids from graded Steinberg algebras

We show how to reconstruct a graded ample Hausdorff groupoid with topologically principal neutrally graded component from the ring structure of its graded Steinberg algebra over any commutative… Expand

The dynamics of Leavitt path algebras

- R. Hazrat
- Mathematics
- 13 September 2012

Recently it was shown that the notion of flow equivalence of shifts of finite type in symbolic dynamics is related to the Morita theory and the Grothendieck group in the theory of Leavitt path… Expand

The talented monoid of a Leavitt path algebra

- R. Hazrat, Huanhuan Li
- Mathematics
- 22 March 2019

There is a tight relation between the geometry of a directed graph and the algebraic structure of a Leavitt path algebra associated to it. In this note, we show a similar connection between the… Expand

The graded structure of Leavitt path algebras

- R. Hazrat
- Mathematics
- 11 May 2010

A Leavitt path algebra associates to a directed graph a ℤ-graded algebra and in its simplest form it recovers the Leavitt algebra L(1, k). In this note, we first study this ℤ-grading and characterize… Expand

On graded irreducible representations of Leavitt path algebras

- R. Hazrat, K. Rangaswamy
- Mathematics
- 21 July 2015

Using the E-algebraic systems, various graded irreducible representations of a Leavitt path algebra L of a graph E over a field K are constructed. The concept of a Laurent vertex is introduced and it… Expand

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