Bilinear forms, Clifford algebras, \(q\)-commutation relations, and quantum groups

DOI10.1006/jabr.1999.8257zbMath0960.16044OpenAlexW1986985715MaRDI QIDQ1570876

Keith C. Hannabuss

Publication date: 7 February 2001

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1999.8257

zbMATH Keywords

non-commutative geometryquantum groupsbilinear formsClifford algebrasHeisenberg algebras\(q\)-commutation relationsdeformed enveloping algebrasquantised function spaces

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Clifford algebras, spinors (15A66) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Quadratic and bilinear forms, inner products (15A63)

Related Items (1)

Clifford algebra of an antiautomorphism

Cites Work

• Q-analogues of Clifford and Weyl algebras - spinor and oscillator representations of quantum enveloping algebras
• Twisted second quantization
• Three-dimensional hyperbolic geometry as \(\infty\)-adic Arakelov geometry
• Quantum differentials and the \(q\)-monopole revisited
• Positive representations of general commutation relations allowing Wick ordering
• Coherent states of the \(q\)-canonical commutation relations
• Tomita's theory of modular Hilbert algebras and its applications
• The quantum group SU_q(2) and a q-analogue of the boson operators
• Quantum linear groups
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