|XXXVIII Workshop on Geometric Methods in Physics||30.06-6.07.2019|
|VIII School on Geometry and Physics||24-28.06.2019|
Participants of Workshop
Participants of School
Classification of twisted cocycles
Classification of Lie algebras is a complicated task with difficulty rapidly growing with their dimension. Complete classification is known up to dimension 6 only. Even in low dimensional cases, whenever there appears parametric continuum, distinguishing non-isomorphic algebras is demanding. One of the tools which simplifies the isomorphism problem are invariant characteristics, for example dimensions of the vector spaces of the standard cohomology cocycles. In order to obtain more invariants, the definition of cocycles is modified. The complete classification of the resulting twisted cocycles up to dimension 3 is presented as well as their role in classification of low-dimensional Lie algebras.
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