Bilinear forms, Clifford algebras, $q$-commutation relations, and quantum groups

Constructions are described which associate algebras to arbitrary bilinear forms, generalising the usual Clifford and Heisenberg algebras. Quantum groups of symmetries are discussed, both as deformed enveloping algebras and as quantised function spaces. A classification of the equivalence classes of bilinear forms is also given. © 2000 Academic Press