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Everything about Algebra representation
Study of abstract algebraic structures
In abstract algebra, a representation of an associative algebra is a module for that algebra. Here an associative algebra is a ring. If the algebra is not unital, it may be made so in a standard way ; there is no essential difference between modules for the resulting unital ring, in which the identity acts by the identity mapping, and representations of the algebra. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Algebra representationA 5-minute orientation
- Skim a recent paper: A Lie algebra representation for efficient 2D shape classificationInfluential work since 2022
- Pick up a classic book: Elements of the representation theory of associative algebrasThe most-reprinted book on the subject
- Read the landmark paper: Algebraic Representation of Thermodynamic Properties and the Classification of SolutionsCited 5,587 times
- Go sideways: Diagonal matrixA closely related topic
- Go sideways: Eigenvalues and eigenvectorsA closely related topic
🏆 Landmark papers (most cited)
Algebraic Representation of Thermodynamic Properties and the Classification of Solutions
Representation of Local Current Algebra at Infinite Momentum
Factorizable Representation of Current Algebra
Representation of Elliptic Operators in an Enveloping Algebra
The modular representation algebra of a finite group
A representation theory for commutative topological algebra
Representation theory of the 0-Hecke algebra
Image algebra representation of parallel optical binary arithmetic
🆕 Influential since 2022
A Lie algebra representation for efficient 2D shape classification
Symmetric Functions and 3D Fermion Representation of $$\pmb {W_{1+\infty }}$$ Algebra
Yang–Baxter algebra and MacMahon representation
Graph Geometric Algebra networks for graph representation learning
On the Representation of Semigroup C*-Algebra as a Crossed Product
📚 Books worth reading
Elements of the representation theory of associative algebrasDaniel Simson, Andrzej Skowronski · 2007
Pseudoreductive GroupsBrian Conrad · 2010
Abelian l̳-adic representations and elliptic curvesJean-Pierre Serre · 1968- 📕Linear Algebra and Group RepresentationsRonald Shaw · 1982
Representations of AlgebrasFlavio Ulhoa Coelho, Hector Goldschimdt · 2001- 📕Differential Tensor Algebras and Their Module CategoriesR. Bautista, L. Salmeròn · 2009
Poisson geometry, deformation quantisation and group representationsDaniel Sternheimer, N. J. Hitchin · 2005
Representation theory of finite groups and associative algebrasCharles W. Curtis · 1962
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Diagonal matrix In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices…
- Eigenvalues and eigenvectors In linear algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a (nonzero) vector that has its direction unchanged (or reversed) by…
- Representation theory of SU(2) In the study of the representation theory of Lie groups, the study of representations of SU(2) is fundamental to the study of representations of semisimple…
- Associative algebra In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center…
- Spectral theorem In linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented…
- Representation theory of semisimple Lie algebras In mathematics, the representation theory of semisimple Lie algebras is one of the crowning achievements of the theory of Lie groups and Lie algebras.…
- Vector space In mathematics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled")…
- Linear algebra Linear algebra is the branch of mathematics concerning linear equations such as a1x1+⋯+anxn=b, linear maps such as the following: (x1,…,xn)↦a1x1+⋯+anxn…