Register to reply

Adjoint representations and Lie Algebras

by countable
Tags: adjoint, algebras, representations
Share this thread:
Mar13-11, 09:02 AM
P: 13
I have a very superficial understanding of this subject so apologies in advance for what's probably a stupid question.

Can someone please explain to me why if we have a Lie Group, G with elements g, the adjoint representation of something, eg [tex]g^{-1} A_\mu g[/tex] takes values in the Lie Algebra of G?

Ie. Why does it necessarily mean that [tex][A_\mu,A_\nu]=if_{ijk}A_\sigma[/tex] where f is the structure constant

Phys.Org News Partner Mathematics news on
Researcher figures out how sharks manage to act like math geniuses
Math journal puts Rauzy fractcal image on the cover
Heat distributions help researchers to understand curved space
Mar16-11, 10:01 AM
P: 13

Register to reply

Related Discussions
Griffiths IEP adjoint operator vs. Scadron's Advanced Quantum Theory adjoint operator Advanced Physics Homework 0
Algebras and Sigma-Algebras Set Theory, Logic, Probability, Statistics 3
Representations of algebras? Linear & Abstract Algebra 12
Proving that the Composition of Two Self-Adjoint Operators is Self-Adjoint Calculus & Beyond Homework 2
Prove there are exactly 4 non-isomorphic algebras among algebras Af Calculus & Beyond Homework 0