On certain realizations of the \(q\)-deformed exterior differential calculus

DOI10.1016/S0034-4877(99)80026-3zbMath0934.58007OpenAlexW2054485746MaRDI QIDQ1305709

Richard Kerner, Viktor Abramov

Publication date: 9 April 2000

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(99)80026-3

zbMATH Keywords

non-commutative geometry\(q\)-deformationsgauge theorygeneralized Clifford algebras\(Z_N\)-graded algebras

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Noncommutative geometry (à la Connes) (58B34)

Related Items (10)

Noncommutative Galois extension and graded \(q\)-differential algebra ⋮ A differential calculus on the \(\mathbb{Z}_3\)-graded quantum group \(\mathrm{GL}_q(2)\) ⋮ CARTAN CALCULUS OF Z₃-GRADED DIFFERENTIAL CALCULUS ON THE QUANTUM PLANE ⋮ Differential geometry of the \(\mathbb Z_3\)-graded quantum supergroup \(\mathrm{GL}_{q,j}(1|1)\) ⋮ Differential calculi on \(\mathbb Z_3\)-graded Grassmann plane ⋮ Semi-commutative Galois Extension and Reduced Quantum Plane ⋮ The Hopf algebra structure of the Z3-graded quantum supergroup GLq,j(1∣1) ⋮ A differential calculus on the (\(h, j\))-deformed \(\mathrm {Z}_3\)-graded superplane ⋮ On a graded q-differential algebra ⋮ QUANTUM GROUPS AND DIFFERENTIAL FORMS

Cites Work

• Unnamed Item
• Superconnections, Thom classes, and equivariant differential forms
• Covariant \(q\)-differential calculus and its deformations at \(q^N=1\)
• Generalized Clifford algebras and hyperspin manifolds
• Universal \(Z_N\)-graded differential calculus
• \(\mathbb{Z}_ 3\)-graded exterior differential calculus and gauge theories of higher order
• The cubic chessboard
• Hypersymmetry: A ℤ3-graded generalization of supersymmetry

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