Solution

Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 5 / 2 / Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 3 / 8 / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 3 / 2 / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 3 / 5 / Solution

{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 $k$.

Codex @codex  0

 Incoming links: Central character of a block