# Index
[[Abelian algebras]]
[[Abelian groups]]
[[Algebras]]
[[Algebra representation]]
[[algebraic structure]]
[[Anti-commutator]]
[Associative algebras](Associative%20algebras.md)
[Automorphisms](Automorphisms.md)
[Clifford algebra](Clifford%20algebra.md)
[Commutative rings](Commutative%20rings)
[[Commutators]]
[[Complex vector spaces]]
[[Connected topological groups]]
[[Continuous groups]]
[Cyclic group](Cyclic%20group.md)
[[Dihedral groups]]
[[Direct sum]]
[Direct sum of group representations](Direct%20sum%20of%20group%20representations)
[[Finite group]]
[[GL(n;F)]]
[[Group representation]]
[[Groups]]
[Group axioms](Group%20axioms.md)
[Group-like structure](Group-like%20structure)
[[Homomorphism]]
[Idempotence](Idempotence)
[[Induced operation]]
[[Infinite group]]
[[Irredicucible representation]]
[[Isomorphisms]]
[[Jacobi identity]]
[[Kernel]]
[Linear map](Linear%20map.md)
[[Module]]
[Non-associative algebras](Non-associative%20algebras.md)
[[Pauli groups]]
[[Permutation group]]
[[Pointed sets]]
[[Real vector spaces]]
[[Representation]]
[Rings](Rings.md)
[[Simply connected group]]
[[Topological group]]
[[Vector spaces]]
[[Z2 cyclic group]]
[Zero ring](Zero%20ring.md)
## Sub Indices
[[Lie groups, algebras, and representations (Index)]]
[Linear Algebra and Matrix Theory (index)](Linear%20Algebra%20and%20Matrix%20Theory%20(index).md)
---
## Proofs and examples
---
# Basic concepts
## Set theory
## Symmetry
Transformations that preserve structures are themselves referred to as _symmetries._
## Universal algebra
## Category theory
## Algebraic objects
## Fields
## Applications
---
# Bibliography
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[Aluffi, P., _Algebra: Chapter 0_, American Mathematical Society, 2009](Aluffi,%20P.,%20Algebra%20Chapter%200,%20American%20Mathematical%20Society,%202009.md)
[Axler, S., Down With Determinants, _American Mathematical Monthly 102_, 1995.](Axler,%20S.,%20Down%20With%20Determinants,%20American%20Mathematical%20Monthly%20102,%201995..md)
[Axler S., Gerhing F.W., Ribet K.A. _Linear Algebra Done Right_, Springer, 2nd edition, 1997](Axler%20S.,%20Gerhing%20F.W.,%20Ribet%20K.A.%20Linear%20Algebra%20Done%20Right,%20Springer,%202nd%20edition,%201997.md)
[Cherney D., Denton T., and Waldron A., _Linear Algebra_, 2013](Cherney%20D.,%20Denton%20T.,%20and%20Waldron%20A.,%20Linear%20Algebra,%202013..md)
[Griffiths D. J., _Introduction to Quantum Mechanics_, Pearson Prentice Hall, 2nd edition, 2005.](Griffiths%20D.%20J.,%20Introduction%20to%20Quantum%20Mechanics,%20Pearson%20Prentice%20Hall,%202nd%20edition,%202005..md)
[Hall, B., _Lie Groups Lie Algebras and Representations_, Springer, 2nd edition, 2015.](Hall,%20B.,%20Lie%20Groups%20Lie%20Algebras%20and%20Representations,%20Springer,%202nd%20edition,%202015..md)
[Jänich K., _Topology_. Translated by Silvio Levy, Springer-Verlag 1984](Jänich%20K.,%20Topology.%20Translated%20by%20Silvio%20Levy,%20Springer-Verlag,%201984.md)
[joshphysics (https://physics.stackexchange.com/users/19976/joshphysics), Trace of an operator matrix (Quantum computation and quantum information), URL (version: 2015-04-24): https://physics.stackexchange.com/q/104155](joshphysics%20Trace%20of%20an%20operator%20matrix%20(Quantum%20computation%20and%20quantum%20information),%20URL%20(version%202015-04-24).md)
[Kuttler K., _Elementary Linear Algebra_, 2021.](Kuttler%20K.,%20Elementary%20Linear%20Algebra,%202021..md)
[Nielson, M. A., Chuang, I. L. _Quantum Computation and Quantum Information_, Cambridge University Press, 2010](Nielsen,%20M.%20A.,%20Chuang,%20I.%20L.%20Quantum%20Computation%20and%20Quantum%20Information,%20Cambridge%20University%20Press,%202010.md)
[Schollwöck, U. Homework 1, _Quantum Mechanics 1_ (German) (2019-2020)](Schollwöck,%20U.%20Homework%201,%20Quantum%20Mechanics%201%20(German)%20(2019-2020).md)
Hatcher. A. _Algebraic Topology_
Fraleigh, J. B, Katz, V. J. _A First Course in Abstract Algebra_
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%20-%20Quantum%20Theory%20for%20Mathematicians%20(2013,%20Springer-Verlag%20New%20York)%20-%20libgen.lc.pdf)
Schollwöck, U., Homework 0, Quantum Mechanics 1 (German) (2019/2020)
Horn R. A., Johnson C. A., _Matrix Analysis_
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Istratescu, V. I. _Inner Product Structures: Theory and Application_
%20-%20Inner%20Product%20Structures_%20Theory%20and%20Applications%20(1987,%20Springer%20Netherlands)%20-%20libgen.lc.pdf)
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[von Neumann J., _Mathematical Foundations of Quantum Mechanics_. Translated by Robert T. Beyer. Princeton University Press, 2018.](von%20Neumann%20J.,%20Mathematical%20Foundations%20of%20Quantum%20Mechanics.%20Translated%20by%20Robert%20T.%20Beyer.%20Princeton%20University%20Press,%202018..md)
[Woit, Peter. _Quantum Theory, Groups and Representations: An Introduction_, Springer, 2017](Woit,%20Peter.%20Quantum%20Theory,%20Groups%20and%20Representations%20An%20Introduction,%20Springer,%202017.md)
#MathematicalFoundations/Algebra/AbstractAlgebra
#MathematicalFoundations/Algebra/AbstractAlgebra/Algebras
#MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory
#MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Groups
#MathematicalFoundations/Algebra/AbstractAlgebra/RepresentationTheory
#MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Lie/LieGroups
#MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Lie/LieGroups/Algebras
#MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra
#MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/VectorSpaces
#MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/Operators
#MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/Operators/Matrices
#MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/MultiLinearAlgebra
#MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/MultiLinearAlgebra/Tensors
#Bibliography
#index