# Glossary

### # lifts / $\mathcal{O}$
The number of $\mathcal{O}$-Morita equivalence classes of blocks reducing to a representative of the given $k$-class.
Let $R$ be a commutative ring and $A$ an $R$-algebra. The Picard group ${\rm Pic}_R(A)$ has elements isomorphism classes of $A$-$A$-bimodules inducing a Morita equivalence, with multiplication given by taking tensor products over $A$.
Given a cyclic $p$-group $P$, the Brauer trees whose vertex multiplicities add to $|P|$, where non-exceptional vertices are regarded as having multiplicity $1$.