A. Alekseev
Inst. Theor. Physics, University of Uppsala, Box 803
S-75108 Uppsala, Sweden
Abstract:
Two elementary finite-dimensional examples of quantization are of great importance:
a) Quantization of the exterior algebra xixj+xjxi=0 to the Clifford algebra xixj+xjxidij.
b) Quantization of the symmetric algebra xixj-xjxi=0 to the universal enveloping algebra xi xj-xj xi=fijkxk of a Lie algebra.
We show how these two examples give clues to understanding of several
topics in modern mathematical physics including the theory of dynamical
r-matrices and the relation between quantization and homotopy. We discuss
physical applications to topological field theory and to the black hole
physics.