Group Algebras¶
This module implements the category of group algebras for arbitrary
groups over arbitrary commutative rings. For details, see
sage.categories.algebra_functor
.
AUTHOR:
- David Loeffler (2008-08-24): initial version
- Martin Raum (2009-08): update to use new coercion model – see trac ticket #6670.
- John Palmieri (2011-07): more updates to coercion, categories, etc., group algebras constructed using CombinatorialFreeModule – see trac ticket #6670.
- Nicolas M. Thiéry (2010-2017), Travis Scrimshaw (2017): generalization to a covariant functorial construction for monoid algebras, and beyond – see e.g. trac ticket #18700.
-
sage.categories.group_algebras.
GroupAlgebras
¶ The category of group algebras over a given base ring.
EXAMPLES:
sage: C = Groups().Algebras(ZZ); C Category of group algebras over Integer Ring sage: C.super_categories() [Category of hopf algebras with basis over Integer Ring, Category of monoid algebras over Integer Ring]
We can also construct this category with:
sage: C is GroupAlgebras(ZZ) True
Here is how to create the group algebra of a group \(G\):
sage: G = DihedralGroup(5) sage: QG = G.algebra(QQ); QG Algebra of Dihedral group of order 10 as a permutation group over Rational Field
and an example of computation:
sage: g = G.an_element(); g (1,4)(2,3) sage: (QG.term(g) + 1)**3 4*() + 4*(1,4)(2,3)
Todo
- Check which methods would be better located in
Monoid.Algebras
orGroups.Finite.Algebras
.
- Check which methods would be better located in