Details:
Title  A Gr\"obnerbases algorithm for the computation of the cohomology of Lie (super) algebras.  Author(s)  Mansour Aghasi, Benyamin M.Alizadeh, Joël Merker, Masoud Sabzevari  Type  Article in Journal  Abstract  We present an effective algorithm for computing the standard cohomology spaces of finitely generated Lie (super) algebras over a 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 Gröbner 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 CartanTanaka connections.  Keywords  Lie (super) algebras, cohomology, reduced Gröbner bases, quotient vector spaces, homogeneity splitting  ISSN  01887009; 16614909/e 
URL 
http://link.springer.com/article/10.1007%2Fs000060110319z 
Language  English  Journal  Adv. Appl. Clifford Algebr.  Volume  22  Number  4  Pages  911937  Publisher  Springer (Birkh\"auser), Basel  Year  2012  Edition  0  Translation 
No  Refereed 
No 
