Quantum Clifford algebras from spinor representations
Copyright policy )Quantum Clifford algebras from spinor representations
A general theory of quantum Clifford algebras is presented, based on a quantum generalization of the Cartan theory of spinors. We concentrate on the case when it is possible to apply the quantum-group formalism of bicovariant bimodules. The general theory is then singularized to the quantum SL(n,C) group case, to generate explicit forms for the whole class of braidings required. The corresponding spinor representations are introduced and investigated. Starting from our Clifford algebras we introduce the quantum-Euclidean underlying spaces compatible with different choices of *-structures from where the analogues of Dirac and Laplace operators are built. Using the formalism developed, quantum Spin(n) groups are defined.
spinor representations, quantum groups, braided monoidal category, \(q\)-calculus, quantum Clifford algebras, Quantum groups (quantized enveloping algebras) and related deformations, quantum spin groups, Clifford algebras, spinors, \(q\)-space, Applications of matrix theory to physics, \(*\)-structures, Quantum groups and related algebraic methods applied to problems in quantum theory, Hecke algebras, Spinor and twistor methods applied to problems in quantum theory, \(q\)-Dirac operators
spinor representations, quantum groups, braided monoidal category, \(q\)-calculus, quantum Clifford algebras, Quantum groups (quantized enveloping algebras) and related deformations, quantum spin groups, Clifford algebras, spinors, \(q\)-space, Applications of matrix theory to physics, \(*\)-structures, Quantum groups and related algebraic methods applied to problems in quantum theory, Hecke algebras, Spinor and twistor methods applied to problems in quantum theory, \(q\)-Dirac operators
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