The Database of Low Dimensional Singer Algebras

The database provides information about the algebras A[q,n,z] that are studied in the papers [BHHK20] and [BHHK21], with z ranging from 1 to 10000.

The following JSON format data files are available. (These files are also GAP readable.)

• The following files contain the information about the parameters z, q, n, m, l, v', d, dec, delta, where n is the multiplicative order of q modulo z, m = m(q,e) (for e = (qⁿ-1)/z), l is the Loewy length, and v' encodes the Loewy vector.

  1 ≤ z ≤   500 : lvdata01.json   501 ≤ z ≤ 1000 : lvdata02.json 1001 ≤ z ≤ 1500 : lvdata03.json 1501 ≤ z ≤ 2000 : lvdata04.json 2001 ≤ z ≤ 2500 : lvdata05.json 2501 ≤ z ≤ 3000 : lvdata06.json 3001 ≤ z ≤ 3500 : lvdata07.json 3501 ≤ z ≤ 4000 : lvdata08.json 4001 ≤ z ≤ 4500 : lvdata09.json 4501 ≤ z ≤ 5000 : lvdata10.json

  5001 ≤ z ≤   5500 : lvdata11.json 5501 ≤ z ≤   6000 : lvdata12.json 6001 ≤ z ≤   6500 : lvdata13.json 6501 ≤ z ≤   7000 : lvdata14.json 7001 ≤ z ≤   7500 : lvdata15.json 7501 ≤ z ≤   8000 : lvdata16.json 8001 ≤ z ≤   8500 : lvdata17.json 8501 ≤ z ≤   9000 : lvdata18.json 9001 ≤ z ≤   9500 : lvdata19.json 9501 ≤ z ≤ 10000 : lvdata20.json

• The values m(q,e) for small e are collected in mqe.json.

• The canonical isomorphisms between entries are collected in joinsCan.json.

• The non-canonical permutation isomorphisms between entries are collected in joinsPerm.json. The information about the permutations is stored in joinsPermExt.json.

• The proofs of nonisomorphism are collected in splitsComb.json and splitsOther.json.

• The currently open questions about the classification up to isomorphism are collected in opencases.json.

File created on 10-Jan-2020 by Thomas Breuer.
Last modified on 19-Jul-2021 by Thomas Breuer.