Multiplicative structure of Kauffman bracket skein module quantizations

Details Multiplicative structure of Kauffman bracket skein module quantizations Multiplicative structure of Kauffman bracket skein module quantizations

1999-02-20

arxiv.org/abs/math/9902117v1

Mathematics

Quantum Algebra

Scientific paper

We describe, for a few small examples, the Kauffman bracket skein algebra of a surface crossed with an interval. If the surface is a punctured torus the result is a quantization of the symmetric algebra in three variables (and an algebra closely related to a cyclic quantization of $U(so_3$). For a torus without boundary we obtain a quantization of "the symmetric homologies" of a torus (equivalently, the coordinate ring of the $SL_2(C)$-character variety of $Z \oplus Z$). Presentations are also given for the four punctured sphere and twice punctured torus. We conclude with an investigation of central elements and zero divisors.

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