The quantum orthogonal mystery

TL;DR

This paper explores the application of non-commutative differential calculus to construct quantum groups, specifically orthogonal quantum groups, highlighting differences from classical Lie algebras.

Contribution

It introduces methods for constructing orthogonal quantum Lie algebras using non-commutative calculus, revealing dimension differences from classical counterparts.

Findings

Quantum groups can be constructed via non-commutative calculus.

Orthogonal quantum groups exhibit different dimensions than classical Lie algebras.

Multiple methods for constructing orthogonal quantum Lie algebras are described.

Abstract

This is (hopefully) a Latexable version of a talk given at the XXX Winter School in Theoretical Physics at Karpacz in February 1994. It discusses the use of non-commutative differential calculus to construct a Lie algebra of a quantum group. Usually the result has a different dimension from the classical Lie algebra. This is illustrated by menas of the orthogonal quantum group, and various other possible ways of constructing an orthogonal Lie algebra are described.