nLab
exceptional isomorphism

Contents

Context

Equality and Equivalence

Exceptional structures

Contents

Idea

Given a sequence of structures following some pattern, one loosely calls isomorphisms that pertain to some special elements in the sequence, without themselves following that pattern, exceptional or sporadic.

Examples

Spin groups

The archetypical example is isomorphisms of spin groups. These appear in the infinite sequence {Spin(p)|p}\big\{Spin(p) \vert p \in \mathbb{N}\big\}, and for low values of pp, but not generally, there are isomorphisms to other classical Lie groups.

See at spin group – Exceptional isomorphisms.

Finite linear groups

There is an exceptional isomorphisms

PSL 2(𝔽 5)IPSL_2(\mathbb{F}_5) \;\simeq\; I

between the projective special linear group over the prime field 𝔽 5\mathbb{F}_5 with the icosahedral group.

See at Icosahedral group – Exceptional isomorphism to PSL(F5).

Created on May 14, 2019 at 00:26:00. See the history of this page for a list of all contributions to it.