Bianchi group

For the 3-dimensional Lie groups or Lie algebras, see Bianchi classification.

In mathematics, a Bianchi group is a group of the form

PSL₂(O_d)

where d is a positive square-free integer. Here, PSL denotes the projective special linear group and O_d is the ring of integers of the imaginary quadratic field Q(√−d).

The groups were first studied by Luigi Bianchi in the 1890s as a natural class of discrete subgroups of PSL₂(C).

References

B.Fine (2001), "Bianchi group", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1556080104, http://www.encyclopediaofmath.org/index.php?title=B/b110500

External links

Allen Hatcher, Bianchi Orbifolds