Paper Info
Title
A Modular Algorithm for Computing Cohomologies of Lie Algebras and Superalgebras
Abstract
The paper describes an improved algorithm for computing cohomologies of Lie (super)algebras. The original algorithm developed earlier by the author of this paper is based on the decomposition of the entire cochain complex into minimal subcomplexes. The suggested improvement consists in the replacement of the arithmetic of rational or integer numbers by a more efficient arithmetic of modular fields and the use of the relationship dim Hk(\mathbb{F}p) ≥ dimHk(\mathbb{Q}) between the dimensions of cohomologies over an arbitrary modular field \mathbb{F}p = \mathbb{Z}/p\mathbb{Z} and the filed of rational numbers \mathbb{Q}. This inequality allows us to rapidly find subcomplexes for which dimHk(\mathbb{F}p) 0 (the number of such subcomplexes is usually not great) using computations over an arbitrary \mathbb{F}p and, then, carry out all required computations over \mathbb{Q} in these subcomplexes.
Year
DOI
Venue
2004
10.1023/B:PACS.0000029580.59590.ae
Programming and Computer Software
Keywords
DocType
Volume
minimal subcomplexes,modular algorithm,entire cochain complex,computing cohomologies,relationship dim hk,improved algorithm,integer number,arbitrary modular field,rational number,efficient arithmetic,lie algebras,modular field,original algorithm,lie algebra
Journal
30
Issue
ISSN
Citations 
3
1608-3261
0
PageRank 
References 
Authors
0.34
2
1
Name
Order
Citations
PageRank
V. V. Kornyak11212.76