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Graded Rings and Graded Grothendieck Groups
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 versusExpand
Mathematica: A Problem-Centered Approach
This book introduces the vast array of features and powerful mathematical functions of Mathematica using a multitude of clearly presented examples and worked- out problems to enable the reader to learn from the codes, thus avoiding long and exhausting explanations. Expand
The graded Grothendieck group and the classification of Leavitt path algebras
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
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
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 theExpand
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 commutativeExpand
The dynamics of Leavitt path algebras
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 pathExpand
The talented monoid of a Leavitt path algebra
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 theExpand
The graded structure of Leavitt path algebras
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 characterizeExpand
On graded irreducible representations of Leavitt path algebras
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 itExpand