Research

    Current research

        My general interests are Differential Geometry and Topology, Non-Euclidean Spaces, Fibrations. Now, I study modules over
        algebra and their properties. More concretely, only non-isomorphic irreducible three dimentional algebras are considered and
        their corresponding free modules. In the future, I plan to enlarge this study also to four-dimensional algebras.

    List of publications

       Recent paper:

Trnkova, M.: On principal fibrations associated with one algebra, presented by 28^th Winter School Geometry and Physics, Srni, Czech Republic, January 12-19, 2008, 11pp, arxiv: 0809.0946

        In this paper we study two types of fibrations associated with a 3-dimensional unital associative irreducible algebra and their
          basic properties. We investigate trivial principal fibrations of degenerate semi-Euclidean sphere and their semi-conformal and           projective models. We use Norden normalization method for constructing second model.

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       Papers in Russian:

Dyachkova M.V: The projectivisation of conformal model of non-Euclidean sphere fiber bundle by double numbers subalgebra, «Sbornik trudov mezhdunarodnogo geometricheskogo seminara imeni G.F. Lapteva», Penza, 2007, P. 37-43. (in Russian)
Dyachkova M.V., The non-Euclidean sphere fiber bundle by dual numbers subalgebra and its semiconformal interpretation, "Vestnik Cheboksarskogo gos. ped. instituta", Cheboksary, 2006. (in Russian)
Dyachkova M.V., The sphere principle fiber bundle of 3-algebra and its semiconformal interpretation, Trudy "IV Kolmogorovskih chtenii", Jaroslavl, 2006. (in Russian)

In these papers we study the manifolds over algebras. We describe the examples of principal fibrations of these manifolds and we construct their conformal and projective models.