Algebraic character
In mathematics, an algebraic character is a formal expression attached to a module in representation theory of semisimple Lie algebras that generalizes the character of a finite-dimensional representation and is analogous to the Harish-Chandra character of the representations of semisimple Lie groups. == Definition == Let g {\displaystyle {\mathfrak {g}}} be a semisimple Lie algebra with a fixed Cartan subalgebra h , {\displaystyle {\mathfrak {h}},} and let the abelian group A = Z [ [ h ∗ ] ] {\displaystyle A=\mathbb {Z} [[{\mathfrak {h}}^{*}]]} consist of the (possibly infinite) formal integral linear combinations of e μ {\displaystyle e^{\mu }} , where μ ∈ h ∗ {\displaystyle \mu \in {\mathfrak {h}}^{*}} , the (complex) vector space of weights.