= Central character of a block
{title2=$\omega_b:Z(kG)\to Z(kGb)/J(Z(kGb))$}
= Central characters of a block
{synonym}
The center of an indecomposable finite-dimensional <block of a group algebra> is a commutative <Artinian local ring>. Its quotient by its <Jacobson radical> is a <field>, giving the block's central character. Over a <splitting field for finite group representations> the residue field is the coefficient field; without this assumption one retains the residue field rather than pretending every central character is scalar-valued over $k$.
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