I'm working through some Lie theoretic representation theory, and the definition of a $(\mathfrak{g},K)$-module states that the representation $V$ decomposes into an algebraic direct sum of finite-dimensional invariant subspaces under the action of $K$. My question is, what other types of direct sum should I be concerned about here? Why specify algebraic direct sum?
2026-03-30 02:06:41.1774836401
What is the alternative of an algebraic direct sum?
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