Quantum symmetry modelled through quantum group or its dual, quantum algebra, is a very active field of relevant physical and mathematical research stimulated often by physical intuition and with promising physical applications. This volume gives some information on the progress of this field during the years after the quantum group workshop in Clausthal 1989. Quantum symmetry is connected with very different approaches and views. The field is not yet coherent; there are different notions of quantum groups and of quantum algebras through algebraic deformations of groups and algebras. Hence its development has various directions following more special mathematical and physical interests.
Sample Chapter(s)
Quantum Symmetry in Quantum Theory (279 KB)
Contents:
- Physical Applications of Quantum Symmetries:
- Quantum Symmetry in Quantum Theory (G Mack & V Schomerus)
- Quantum Symmetry Associated with Braid Group Statistics (K-H Rehren)
- Quantum Groups and Quantum Algebras as Symmetries of Dynamical Systems (P P Kulish)
- Quantum Spaces, Quantum Symmetries and Differential Calculi:
- Realizations and Real Forms of Quantum Groups in 2 Dimensions (H Ewen et al)
- Quantum Vectors and Quantum Matrices (A Sudbery)
- Representation of Quantum Algebras and Groups:
- Irreducible Representations of the SUq(3) Quantum Algebra: The Connection between U and T Bases (Yu F Smirnov & A A Malashin)
- Adjoint “Extremal Projectors” and Indecomposable Representations for Uq(Sl(2,C)) (H D Doebner & V N Tolstoy)
- Representations of Quantum Algebras and q-Special Functions (R Floreanini & L Vinet)
- Quantum Deformations and R-Matrices:
- q-Deformations of Noncompact Lie (Super-) Algebras: the Examples of q-Deformed Lorentz, Weyl, Poincaré and (Super-) Conformal Algebras (V K Dobrev)
- R-Matrices from Quantization of Non Semisimple Lie Algebras (M Tarlini)
- On the q-Sugawara Construction for the Virasoro (Super) Algebra (M Chaichian & P Presnajder)
- and other papers
Readership: Mathematical physicists.
