Mathematics – Commutative Algebra
Scientific paper
2011-04-28
Mathematics
Commutative Algebra
23 pages
Scientific paper
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 Z^k/B^k of cocycles Z^k modulo coboundaries B^k, 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 Z^k/B^k 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.
-Alizadeh Benyamin M.
Merker Joel
Sabzevari Masoud
No associations
LandOfFree
A Groebner-bases algorithm for the computation of the cohomology of Lie (super) algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Groebner-bases algorithm for the computation of the cohomology of Lie (super) algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Groebner-bases algorithm for the computation of the cohomology of Lie (super) algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-448938