atlas Library · Script File

`lietypes.at`

Source

atlas-scripts/lietypes.at (90 lines)

Definitions

Loads

<basic.at { for |factors@LieType }
<generics.at
<sort.at

Loaded by

complex.at test_unitarity.at sub_cells.at affine.at conjugate.at isomorphism.at class_tables.at W_order.at

Definitions in source order

`A1`

L5A1 = "A1"

`A2`

L6A2 = "A2"

`A3`

L7A3 = "A3"

`A4`

L8A4 = "A4"

`A5`

L9A5 = "A5"

`A6`

L10A6 = "A6"

`A7`

L11A7 = "A7"

`A8`

L12A8 = "A8"

`B2`

L13B2 = "B2"

`B3`

L14B3 = "B3"

`B4`

L15B4 = "B4"

`B5`

L16B5 = "B5"

`B6`

L17B6 = "B6"

`B7`

L18B7 = "B7"

`B8`

L19B8 = "B8"

`C2`

L20C2 = "C2"

`C3`

L21C3 = "C3"

`C4`

L22C4 = "C4"

`C5`

L23C5 = "C5"

`C6`

L24C6 = "C6"

`C7`

L25C7 = "C7"

`C8`

L26C8 = "C8"

`D2`

L27D2 = "D2"

`D3`

L28D3 = "D3"

`D4`

L29D4 = "D4"

`D5`

L30D5 = "D5"

`D6`

L31D6 = "D6"

`D7`

L32D7 = "D7"

`D8`

L33D8 = "D8"

`E6`

L34E6 = "E6"

`E7`

L35E7 = "E7"

`E8`

L36E8 = "E8"

`F4`

L37F4 = "F4"

`G2`

L38G2 = "G2"

commands related to having a canonical Lie_type L40

`to_canonical`

L42to_canonical (LieType lt) = LieType

sort factors and map C2->B2

`standardize_Lie_type`

L51standardize_Lie_type = to_canonical@LieType

backward compatibility

`is_isomorphic`

L53is_isomorphic (LieType lt0, LieType lt1) = bool

also defined in W_reps.at, isomorphism.at

`is_locally_isomorphic`

L57is_locally_isomorphic (RootDatum rd0,RootDatum rd1) = bool

two complex groups are locally isomorphic iff their Lie type are isomorphic

`nice_format` 2 overloads

L62nice_format (LieType lt) = string

L80nice_format (RootDatum rd) = string

`Cartan_matrix_type`

L83Cartan_matrix_type (RootDatum rd) = (LieType,[int])

`simple_type` 2 overloads

L87simple_type (LieType lt) = (string,int)

when we must have a simple type, undo the plural in |simple_factors|

L90simple_type (RootDatum rd) = (string,int)

Generated from atlas-scripts at commit 648506c (2026-10-13).

lietypes.at