Abstract Algebra: Tensor Products
N.B. Singh
This audiobook is narrated by a digital voice.
"Abstract Algebra: Tensor Products" provides a comprehensive exploration of tensor products within the framework of abstract algebra. Beginning with foundational definitions and universal properties, the book progresses to elucidate their applications across diverse algebraic structures such as modules, vector spaces, and rings. Emphasizing clarity and depth, it navigates through advanced topics including categorical perspectives, functorial properties, and their relevance in fields like quantum mechanics and topology. Through numerous examples, and theoretical insights, this book equips readers with the tools to understand and leverage tensor products as powerful algebraic tools, fostering a deeper appreciation for their role in modern mathematics.
Duration - 3h 21m.
Author - N.B. Singh.
Narrator - Digital Voice Mary G.
Published Date - Monday, 20 January 2025.
Copyright - © 2024 N.B. Singh ©.
Location:
United States
Description:
This audiobook is narrated by a digital voice. "Abstract Algebra: Tensor Products" provides a comprehensive exploration of tensor products within the framework of abstract algebra. Beginning with foundational definitions and universal properties, the book progresses to elucidate their applications across diverse algebraic structures such as modules, vector spaces, and rings. Emphasizing clarity and depth, it navigates through advanced topics including categorical perspectives, functorial properties, and their relevance in fields like quantum mechanics and topology. Through numerous examples, and theoretical insights, this book equips readers with the tools to understand and leverage tensor products as powerful algebraic tools, fostering a deeper appreciation for their role in modern mathematics. Duration - 3h 21m. Author - N.B. Singh. Narrator - Digital Voice Mary G. Published Date - Monday, 20 January 2025. Copyright - © 2024 N.B. Singh ©.
Language:
English
Preface
Duración:00:00:37
Introduction to Tensor Products
Duración:00:00:53
Historical Development
Duración:00:04:12
Motivation and Intuition
Duración:00:04:36
Basic Definitions
Duración:00:04:15
Examples and Counterexamples
Duración:00:05:14
Importance in Algebraic Structures
Duración:00:05:01
Relation to Direct Sum and Homomorphisms
Duración:00:05:19
Summary and Overview
Duración:00:04:45
Tensor Product Spaces
Duración:00:00:49
Construction and Existence
Duración:00:04:48
Properties of Tensor Products
Duración:00:03:31
Basis and Dimension
Duración:00:06:58
Tensor Contraction and Extension
Duración:00:03:25
Symmetric and Exterior Powers
Duración:00:03:21
Applications in Geometry and Physics
Duración:00:02:31
Tensor Algebra
Duración:00:00:59
Algebraic Structures of Tensors
Duración:00:03:06
Tensor Products of Vector Spaces
Duración:00:02:45
Universal Property of Tensor Algebra
Duración:00:02:57
Tensor Rank and Tensor Rank Decomposition
Duración:00:02:58
Non-commutative Algebras and Tensor Products
Duración:00:03:07
Representations and Modules
Duración:00:03:24
Applications in Coding Theory
Duración:00:02:56
Multilinear Maps and Tensors
Duración:00:01:03
Multilinear Forms and Multilinear Maps
Duración:00:03:20
Tensor Product of Multilinear Maps
Duración:00:03:25
Symmetry and Antisymmetry of Tensors
Duración:00:03:37
Algebraic Manipulations with Multilinear Maps
Duración:00:03:50
Tensor Derivatives and Applications
Duración:00:03:05
Decompositions and Canonical Forms
Duración:00:03:34
Computational Techniques and Algorithms
Duración:00:03:37
Tensor Products of Modules
Duración:00:01:03
Module Structures and Tensor Products
Duración:00:03:30
Tensor Product of Module Homomorphisms
Duración:00:02:59
Dual Modules and Tensor Products
Duración:00:04:26
Exact Sequences and Tensor Products
Duración:00:04:24
Injective and Projective Modules
Duración:00:04:38
Tensor Products in Representation Theory
Duración:00:05:12
Applications in Algebraic Geometry
Duración:00:05:14
Universal Property of Tensor Products
Duración:00:01:14
Universal Mapping Property
Duración:00:05:03
Categorical Approach to Tensor Products
Duración:00:05:34
Functorial Properties and Adjunctions
Duración:00:05:34
Tensor Products in Category Theory
Duración:00:05:52
Natural Transformations and Functors
Duración:00:04:25
Coherence Theorems and Equivalences
Duración:00:04:17
Applications in Mathematical Logic
Duración:00:03:41
Applications of Tensor Products
Duración:00:01:15
Tensor Products in Quantum Mechanics
Duración:00:04:12
Tensor Networks and Machine Learning
Duración:00:03:35
Algebraic Structures in Topology
Duración:00:03:25
Applications in Group Cohomology
Duración:00:03:19
Homological Algebra and Tensor Products
Duración:00:03:32
Differential Forms and Tensor Products
Duración:00:03:49
Future Directions and Open Problems
Duración:00:03:34