A Theory of Quantized Fields Based on Orthogonal and Symplectic Clifford Algebras

Orthogonal Symmetries and Clifford Algebras

Involutions of the Clifford algebra of a quadratic space induced by orthogonal symmetries are investigated. 2000 Mathematics Subject Classification: 16W10, 11E39

Orthogonal nets and Clifford algebras

A Clifford algebra model for Möbius geometry is presented. The notion of Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced, and the structure equations for adapted frames are derived. These equations are discretized and the geometry of the occuring discrete nets and sphere congruences is discussed in a conformal setting. This way, the notions of “discrete Ribaucour con...

Quantized Symplectic Actions and W -algebras

With a nilpotent element in a semisimple Lie algebra g one associates a finitely generated associative algebra W called a W -algebra of finite type. This algebra is obtained from the universal enveloping algebra U(g) by a certain Hamiltonian reduction. We observe that W is the invariant algebra for an action of a reductive group G with Lie algebra g on a quantized symplectic affine variety and ...

Quantized Symplectic Oscillator Algebras of Rank One

A quantized symplectic oscillator algebra of rank 1 is a PBW deformation of the smash product of the quantum plane with Uq(sl2). We study its representation theory, and in particular, its category O.

On Clifford Theory of Vertex Operator Algebras