Quantum algebra is one of the top-level
mathematics categories used by the
arXiv
arXiv (pronounced " archive"—the X represents the Greek letter chi ⟨χ⟩) is an open-access repository of electronic preprints and postprints (known as e-prints) approved for posting after moderation, but not peer review. It consists o ...
. It is the study of noncommutative analogues and generalizations of commutative algebras, especially those arising in
Lie theory
In mathematics, the mathematician Sophus Lie ( ) initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory. For instance, the latter subject i ...
.
Subjects include:
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Quantum group
In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebra ...
s
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Skein theories
Skein relations are a mathematical tool used to study knots. A central question in the mathematical theory of knots is whether two knot diagrams represent the same knot. One way to answer the question is using knot polynomials, which are invarian ...
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Operadic algebra
In mathematics, an operad is a structure that consists of abstract operations, each one having a fixed finite number of inputs (arguments) and one output, as well as a specification of how to compose these operations. Given an operad O, one define ...
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Diagrammatic algebra In mathematics, a diagram algebra is an algebraic structure
In mathematics, an algebraic structure consists of a nonempty set ''A'' (called the underlying set, carrier set or domain), a collection of operations on ''A'' (typically binary opera ...
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Quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles a ...
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Racks and quandles
In mathematics, racks and quandles are sets with binary operations satisfying axioms analogous to the Reidemeister moves used to manipulate knot diagrams.
While mainly used to obtain invariants of knots, they can be viewed as algebraic construc ...
See also
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Coherent states in mathematical physics
Coherent states have been introduced in a physical context, first as quasi-classical states in quantum mechanics, then as the backbone of quantum optics and they are described in that spirit in the article Coherent states (see alsoJ-P. Gazeau,'' ...
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Glossary of areas of mathematics
Mathematics is a broad subject that is commonly divided in many areas that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of metho ...
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Mathematics Subject Classification
The Mathematics Subject Classification (MSC) is an alphanumerical classification scheme collaboratively produced by staff of, and based on the coverage of, the two major mathematical reviewing databases, Mathematical Reviews and Zentralblatt MATH. ...
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Ordered type system
Substructural type systems are a family of type systems analogous to substructural logics where one or more of the structural rules are absent or only allowed under controlled circumstances. Such systems are useful for constraining access to syst ...
, a
substructural type system
Substructural type systems are a family of type systems analogous to substructural logics where one or more of the structural rules are absent or only allowed under controlled circumstances. Such systems are useful for constraining access to sys ...
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Outline of mathematics
Mathematics is a field of study that investigates topics such as number, space, structure, and change.
Philosophy Nature
* Definitions of mathematics – Mathematics has no generally accepted definition. Different schools of thought, particu ...
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Quantum logic
In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions inspired by the structure of quantum theory. The field takes as its starting point an observa ...
References
External links
Quantum algebra at arxiv.org
Quantum groups
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