@enumeratio/groupalgebra

Group-algebra extensions for compute-engine: cyclic, dihedral and product groups, their group algebras, conjugacy classes and centres. The group algebra $k[G]$ is the most elementary construction in this section of the catalogue — its basis is just the group's elements — and the point of the package is the centre: a canonical commutative subalgebra spanned by class sums, one per conjugacy class. See the guide.

Declaring

import { ComputeEngine } from "@cortex-js/compute-engine";
import { declareGroupAlgebra } from "@enumeratio/groupalgebra";

const ce = new ComputeEngine();
declareGroupAlgebra(ce);

Heads

• Groups — CyclicGroup, DihedralGroup, PermutationGroup, AlternatingGroup, GroupOrder, GroupGenerators, GroupElements
• The algebra — GroupBasis, ClassSum, ConjugacyClasses
• Permutations — Cycles, PermutationCycles, PermutationList, PermutationReplace, Permute, InversePermutation

src/group.ts also exports the underlying group model (directProduct, isAbelian, isCentral, conjugacyClasses) used directly by @enumeratio/hecke and @enumeratio/diagram for their own symmetric-group bookkeeping.

Usage

GroupIsAbelian(CyclicGroup(6))         // True
GroupIsAbelian(DihedralGroup(4))       // False
IsCentral(DihedralGroup(3), ClassSum(DihedralGroup(3), 2))   // True

Next

The guide walks through why every group's centre is commutative even when the group itself is not, and how the class-sum basis connects to irreducible characters.

Pages

• Group Algebras

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• Source: packages/symbols/algebras/groupalgebra
• Depends on: boxes, engine, structures
• In development, also: config, manifest