Download Quivers and Path Algebras Version 1.27 PDF

TitleQuivers and Path Algebras Version 1.27
LanguageEnglish
File Size615.2 KB
Total Pages156
Table of Contents
                            Introduction
	General aims
	Installation and system requirements
Quickstart
	Example 1 – quivers, path algebras and quotients of path algebras
	Example 2 – Introducing modules
	Example 3 – Constructing modules and module homomorphisms
Quivers
	Information class, Quivers
	Constructing Quivers
	Categories and Properties of Quivers
	Orderings of paths in a quiver
	Attributes and Operations for Quivers
	Categories and Properties of Paths
	Attributes and Operations of Paths
	Attributes of Vertices
	Posets
Path Algebras
	Introduction
	Constructing Path Algebras
	Categories and Properties of Path Algebras
	Attributes and Operations for Path Algebras
	Operations on Path Algebra Elements
	Constructing Quotients of Path Algebras
	Ideals and operations on ideals
	Categories and properties of ideals
	Operations on ideals
	Attributes of ideals
	Categories and Properties of Quotients of Path Algebras
	Attributes and Operations (for Quotients) of Path Algebras
	Attributes and Operations on Elements of Quotients of Path Algebra
	Predefined classes and classes of (quotients of) path algebras
	Opposite algebras
	Tensor products of path algebras
	Finite dimensional algebras over finite fields
	Algebras
	Saving and reading quotients of path algebras to and from a file
Groebner Basis
	Constructing a Groebner Basis
	Categories and Properties of Groebner Basis
	Attributes and Operations for Groebner Basis
	Right Groebner Basis
Right Modules over Path Algebras
	Modules of matrix type
	Categories Of Matrix Modules
	Acting on Module Elements
	Operations on representations
	Special representations
	Functors on representations
	Vertex projective modules and submodules thereof
Homomorphisms of Right Modules over Path Algebras
	Categories and representation of homomorphisms
	Generalities of homomorphisms
	Homomorphisms and modules constructed from homomorphisms and modules
Homological algebra
	Homological algebra
Auslander-Reiten theory
	Almost split sequences and AR-quivers
Chain complexes
	Introduction
	Infinite lists
	Representation of categories
	Making a complex
	Information about a complex
	Transforming and combining complexes
	Chain maps
Projective resolutions and the bounded derived category
	Projective and injective complexes
	The bounded derived category
Combinatorial representation theory
	Introduction
	Different unit forms
Degeneration order for modules in finite type
	Introduction
	Basic definitions
	Defining Auslander-Reiten quiver in finite type
	Elementary operations
	Operations returning families of modules
References
Index
                        

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