PASCAL programs for identification of Lie algebras: Part 3: LEVI decomposition and canonical basis
✍ Scribed by D.W. Rand
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 942 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0010-4655
No coin nor oath required. For personal study only.
✦ Synopsis
RADICAL [1] in order to express L in a standard basis: L is decomposed as a direct sum, each component L' is Levi-dc-Catalogue number: AAXN (LEVI), AAXO (CANONIK) composed, each S(L') is decomposed as a direct sum, the nilradical of each R (L') is calculated, and finally the basis of Programs obtainable from: CPC Program Library, Queen's each nilradical is ordered according to its upper central series. University of Belfast, N. Ireland (see application form in this issue). Method of solution LEVI determines the radical R(L) of L using the orthogonal Computers for which the programs are designed and operable: complement, relative to the Killing form, of the derived algebra Control Data Corporation (CDC) CYBER, Series 170, Models [L,L]. If the quotient algebra L/R(L) is not closed under Lie 835 & 855, Centre de calcul, Umversité de Montréal. Operable multiplication, LEVI modifies its basis in order to close it, thus on any computer on which a PASCAL compiler compatible making it a representative of S(L), the maximal (semi-)simple with the ISO standard is implemented subalgebra of L. This closure is performed using either a system of linear inhomogeneous equations when R( L) is Operating system: NOS/BE Abelian, or a recursive method involving quotienting of L by the derived algebra of the radical, hence reducing the problem Programming language used: PASCAL 6000, Version 4, re-to one of smaller dimension. The program CANONIK uses stricted to to the subset compatible with the ISO standard this same method as well as those described in refs. [1,2]. All three algorithms are summarized in ref [3] and presented in High speed storage required: approx. 220000B for LEVI and detail in ref. [4]. 320000B for CANONIK, depending on the complexity of the calculation Restrictions on the complexity of the problem Integer overflow or lack of memory may occur if dim (L) is No, of bits in a word: 64 large, if the structure constant array is very dense, and/or if the structure constants depend on many parameters. Such No. of lines in combined program and test deck. approximately problems are greatest when CANONIK attempts decomposi-5100 lines in LEVI and 10300 lines in CANONIK, including tion as a direct sum. subprograms taken from the programs RADICAL [1] and SPLIT [2]
Typical running time Varies widely, depending on the complexity of the data. Typi-