{{Short description|Category of mathematics papers in ArXiv}} <!-- {{More citations needed|date=August 2012}} --> {{one source |date=May 2024}} {{user-generated |date=May 2024}} In mathematics, '''quantum algebra''' is the study of noncommutative analogues and generalizations of commutative algebras, especially those arising in Lie theory.<ref>{{Cite web|url=https://mathoverflow.net/a/290525/36146|title=What is quantum algebra?|website=mathoverflow.net|access-date=2018-01-22}}</ref>. It is one of the top-level mathematics categories used by the arXiv, and is a unification of algebraic deformations, Hopf algebras, category theory, topology, noncommutative geometry, and quantum groups within quantum mechanics and quantum field theory.<ref>{{Cite web |title=Quantum Algebra |url=https://arxiv.org/list/math.QA/recent |access-date=2025-10-27 |website=arxiv.org |language=en}}</ref><ref>{{Cite web |title=Quantum Algebra -- from Wolfram Library Archive |url=https://library.wolfram.com/infocenter/MathSource/4898/ |access-date=2025-10-27 |website=library.wolfram.com}}</ref><ref>{{Cite web |title=quantum algebra in nLab |url=https://ncatlab.org/nlab/show/quantum+algebra |access-date=2025-10-27 |website=ncatlab.org}}</ref>
Subjects include: *Quantum groups *Skein theories *Operadic algebra *Diagrammatic algebra *Quantum field theory *Racks and quandles
== See also == {{Portal|Mathematics|Science|Technology}} {{div col}} *Coherent states in mathematical physics *Glossary of areas of mathematics *Mathematics Subject Classification *Ordered type system, a substructural type system *Outline of mathematics *Quantum logic {{div col end}}
==References== {{Reflist}}
==External links== *[https://arxiv.org/list/math.QA/current Quantum algebra at arxiv.org]
Category:Quantum groups
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