A non-abelian generalization of the usual formulas for bosonization of fermions in 1+1 dimensions is presented. Any fermi theory in 1+1 dimensions is equivalent to a local bose theory which manifestly possesses all the symmetries of the fermi theory.

https://projecteuclid.org/download/pdf_1/euclid.cmp/1103940923

Nonabelian Bosonization in Two-Dimensions

This text, drawn from the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-term course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semi-simple rings, Jacobson's theory of the radical representation theory of groups and algebras, prime and semi-prime rings, primitive and semi-primitive rings, division rings, ordered rings, local and semi-local rings, and perfect and semi-perfect rings. By aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation, the author has produced a text which is suitable not only for use in a graduate course, but also for self-study by other interested graduate students. Numerous exercises are also included. This graduate textbook on rings, fields and algebras is intended for graduate students in mathematics.

A first course in noncommutative rings, by T. Y. Lam. Pp. 385. £37 (pb), £62.50 (hb). 2001. ISBN 0 387 95325 6 (pb), 0 387 95183 0 (hb) (Springer-Verlag).

Heterotic string theory (I). The free heterotic string

At first only elementary functions were studied in mathematical analysis. Then new functions were introduced to evaluate integrals. They were named special functions: integral sine, logarithms, the exponential function, the probability integral and so on. Elliptic integrals proved to be the most important. They are connected with rectification of arcs of certain curves. The remarkable idea of Abel to replace these integrals by the corresponding inverse functions led to the creation of the theory of elliptic functions.

Representation of Lie groups and special functions

Basic representations of affine Lie algebras and dual resonance models

We give an explicit construction of the affine Lie algebraA

 1
 (1)
 as an algebra of differential operators on ℂ[x
1,x
3,x
5, ...]. This algebra is spanned by the creation and annihilation operators and by the homogeneous components of a certain “exponential generating function” which is strikingly similar to the vertex operator in the string model.

/pdf/construction-of-the-affine-lie-algebra-a1-1-2ic97czz81.pdf

Robert Lee Wilson

Papers

Construction of the affine Lie algebra A1 (1)

The structure of standard modules, I: Universal algebras and the Rogers-Ramanujan identities

Realization of the basic representations of the Euclidean Lie algebras

The structure of standard modules. II. The case A1(1), principal gradation.

Classification of the restricted simple Lie algebras