A string construction of a commutative non-associative algebra related to the exceptional Jordan algebra

The exceptional Jordan algebra and the matrix string

ABSTRACT A new matrix model is described, based on the exceptional Jordan algebra, J3 O . The action is cubic, as in matrix Chern-Simons theory. We describe a compactification that, we argue, reproduces, at the one loop level, an octonionic compactification of the matrix string theory in which SO(8) is broken to G2. There are 27 matrix degrees of freedom, which under Spin(8) transform as the ve...

Cubic Rings and the Exceptional Jordan Algebra

In a previous paper [EG] we described an integral structure (J, E) on the exceptional Jordan algebra of Hermitian 3 × 3 matrices over the Cayley octonions. Here we use modular forms and Niemeier’s classification of even unimodular lattices of rank 24 to further investigate J and the integral, even lattice J0 = (ZE) in J . Specifically, we study ring embeddings of totally real cubic rings A into...

Non-commutative combinatorial algebra

Commutative Algebra Commutative Algebra : General

Non-Commutative Black Hole Algebra and String Theory from Gravity

We generalize the action found by ’t Hooft, which describes the gravitational interaction between ingoing and outgoing particles in the neighbourhood of a black hole. The effect of this back-reaction is that of a shock wave, and it provides a mechanism for recovering information about the momentum of the incoming particles. The new action also describes particles with transverse momenta and tak...