Contents
Introduction 1
Chapter 1. The Definition and Some Basic Properties of the Algebra H[rr] 15
Chapter 2. A Decomposition of the Algebra H[rr] when
~ E
k 21
Chapter 3. Structure of the Algebra H[rr] for Two-Generator Groups 29
Chapter 4. Absolutely Irreducible S£(2) Representations of Two-Generator
Groups 39
Chapter 5. Further Identities in the Algebra H[rr] when
~
E k 47
Chapter 6. Structure of
H+[rrn]
for Free Groups
1fn
59
Chapter 7. Quaternion Algebra Localizations of H[rr] and Absolutely Irreducible
S£(2) Representations 69
Chapter 8. Algebro-Geometric Interpretation of S£(2) Representations of
a~~ ~
Chapter 9. The Universal Matrix Representation of the Algebra H[rr] 89
Chapter 10. Some Knot Invariants Derived from the Algebra H[rr]
Appendix A. Addenda
1*. Addendum to Chapter 1
2*. Addendum to Chapter 2
3*. Addendum to Chapter 3
4*. Addendum to Chapter 4
5*. Addendum to Chapter 5
6*. Addendum to Chapter 6
7*. Addendum to Chapter 7
8*. Addendum to Chapter 8
9*. Addendum to Chapter 9
Appendix B. Afterword
Bibliography
vii
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107
107
110
113
116
130
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