Slovenian Real Algebra Group


Introduction
Members
Publications
Preprints
Visitors
Software
Links





Last change: 9 Jul 2012

Introduction

Real algebra is a branch of algebra which studies formally real rings, i. e. commutative unital rings in which -1 is not a sum of squares. The most important invariant of a formally real ring A is its real spectrum Sper(A). The motivation for studying real algebra comes from semialgebraic geometry. Related areas of algebra are:

  • ordered rings
  • valuation theory
  • quadratic forms

The main interest of the Slovenian real algebra group is noncommutative real algebra. An associative unital ring A is formally real if -1 is not a sum of permuted products of squares. Noncommutative formally real rings include:

  • enveloping algebras of real Lie algebras,
  • group rings of ordered groups,
  • large classes of quantum groups (including quantum polynomials),
  • large classes of rings of differential operators (including real Weyl algebras).
Recommended reading