I'm studying Lie theory from Brian C. Hall's "Lie Groups, Lie Algebras, and Representations," in which he focuses on matrix Lie groups (defined as sets of matrices) rather than general Lie groups (defined as smooth manifolds). He proves that all matrix Lie groups are also general Lie groups, but that the converse doesn't hold: not all Lie groups can be represented as matrix Lie groups. He even gives two examples, though his examples seem fairly obscure to me. Hence my question:
Is there any example of a Lie group that cannot be represented as a matrix Lie group and also has an application in physics?