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Quantum Algebra and Quantum Computers

Abelian and Non-Abelian Structures in Algebraic Mathematics

Algebraic Logic: Boolean logic; Algebraic logic; Łukasiewicz logic; Intuitionistic logic; Mathematical logic; Heyting arithmetic; Metatheory; Metalogic
Quantum Logics and Quantum Computers: Multi-valued logic; Quantum logic; Quantum computer
Quantum Algebra and Standard Model: Quantum affine algebra; Clifford algebra; Von Neumann algebra; C*-algebra; Affine Lie algebra; Kac–Moody algebra; Hopf algebra; Quantum group; Group representation; Unitary representation; Representation theory of the Lorentz group; Stone–von Neumann theorem; Peter–Weyl theorem; Quasi-Hopf algebra; Quasitriangular Hopf algebra; Ribbon Hopf algebra; Quasi-triangular Quasi-Hopf algebra; Quantum inverse scattering method; Exterior algebra; Supergroup; Superalgebra; Yangian; Standard Model; Noncommutative quantum field theory; Noncommutative standard model; Noncommutative geometry
Abstract Algebra: Abstract algebra; Universal algebra; Heyting algebra; MV-algebra; Group algebra; Lie algebra; Lie group; Lie algebroid
Algebraic Topology, Group Theory and Groupoids: Algebraic topology; Groupoid; Group theory; Abelian group; Galois group; Grothendieck group; Esquisse d'un Programme; Galois theory; Grothendieck's Galois theory; Galois cohomology; Homological algebra; Homotopical algebra; Cohomology theory; K-theory; Algebraic K-theory; Topological K-theory
Category Theory: Category theory; Category; Dual; Abelian category; Functor; Yoneda lemma; Limit; Adjoint functors; Natural transformation; Variety; Domain theory; Enriched category; Topos; Descent; Stack; Categorical logic
Higher Dimensional Algebras: Higher-dimensional algebra; Higher category theory; Duality