2011/04/28 by Benyamin M.-Alizadeh, -Alizadeh, Benyamin M., Joel Merker +5
Computer Science · Mathematics · Medicine · #17B56 #68U05 #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Cancer Treatment and Pharmacology #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:17B56 #msc:68U05
paper · pdf · doi:10.48550/arxiv.1104.5300
23 pages
arxiv created 2011/04/28 · openalex publication_date 2011/04/28 · arxiv updated 2011/04/29 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We present an effective algorithm for computing the standard cohomology spaces of finitely generated Lie (super) algebras over a commutative field K of characteristic zero. In order to reach explicit representatives of some generators of the quotient space Zk/Bk of cocycles Zk modulo coboundaries Bk, we apply Groebner bases techniques (in the appropriate linear setting) and take advantage of their strength. Moreover, when the considered Lie (super) algebras enjoy a grading -- a case which often happens both in representation theory and in differential geometry --, all cohomology spaces Zk/Bk naturally split up as direct sums of smaller subspaces, and this enables us, for higher dimensional Lie (super) algebras, to improve the computer speed of calculations. Lastly, we implement our algorithm in the Maple software and evaluate its performances via some examples, most of which have several applications in the theory of Cartan-Tanaka connections.