SL2 Representations of Finitely Presented Groups (Contemporary Mathematics)

SL2 Representations of Finitely Presented Groups (Contemporary Mathematics)

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Description

This book is essentially self-contained and requires only a basic abstract algebra course as background. The book includes and extends much of the classical theory of $SL(2)$ representations of groups. Readers will find $SL(2)$Representations of Finitely Presented Groups relevant to geometric theory of three dimensional manifolds, representations of infinite groups, and invariant theory. It features: a new finitely computable invariant $H[\pi]$ associated to groups and used to study the $SL(2)$ representations of $\pi$; and, invariant theory and knot theory related through $SL(2)$ representations of knot groups.

Contents

The definition and some basic properties of the algebra $H[\pi]$ A decomposition of the algebra $H[\pi]$ when $\frac 12\in k$ Structure of the algebra $H[\pi]$ for two-generator groups Absolutely irreducible $SL(2)$ representations of two-generator groups Further identities in the algebra $H[\pi]$ when $\frac 12\in k$ Structure of $H^+[\pi n]$ for free groups $\pi n$ Quaternion algebra localizations of $H[\pi]$ and absolutely irreducible $SL(2)$ representations Algebro-geometric interpretation of $SL(2)$ representations of groups The universal matrix representation of the algebra $H[\pi]$ Some knot invariants derived from the algebra $H[\pi]$ Appendix A Appendix B References.

Product Details

  • ISBN13: 9780821804162
  • Format: Paperback
  • ID: 9780821804162
  • ISBN10: 0821804162

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