Braided Geometry of the Conformal Algebra

A braided Yang-Baxter Algebra in a Theory of two coupled Lattice Quantum KdV: algebraic properties and ABA representations.

A braided Yang-Baxter Algebra in a Theory of two coupled Lattice Quantum KdV: algebraic properties and ABA representations. Abstract A generalization of the Yang-Baxter algebra is found in quantizing the mon-odromy matrix of two (m)KdV equations discretized on a space lattice. This braided Yang-Baxter equation still ensures that the transfer matrix generates operators in involution which form t...

Algebra in Braided Tensor Categories and Conformal Field Theory

On Infinitesimal Conformal Transformations of the Tangent Bundles with the Generalized Metric

Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...

Intertwining Operator Algebras and Vertex Tensor Categories for Affine Lie Algebras

0. Introduction. The category of finite direct sums of standard (integrable highest weight) modules of a fixed positive integral level k for an affine Lie algebra ĝ is particularly important from the viewpoint of conformal field theory and related mathematics. Here we call this the category generated by the standard ĝ-modules of level k. A central theme is a braided tensor category structure (i...

Lie Algebras and Braided Geometry

We show that every Lie algebra or superLie algebra has a canonical braiding on it, and that in terms of this its enveloping algebra appears as a flat space with braided-commuting coordinate functions. This also gives a new point of view about q-Minkowski space which arises in a similar way as the enveloping algebra of the braided Lie algebra gl2,q. Our point of view fixes the signature of the m...