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Hypercomplex Algebras and Geometry of Spaces with Fundamental Formof an Arbitrary Order

Mikhail P. Burlakov, Igor M. Burlakov, Marek Jukl (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The article is devoted to a generalization of Clifford and Grassmann algebras for the case of vector spaces over the field of complex numbers. The geometric interpretation of such generalizations are presented. Multieuclidean geometry is considered as well as the importance of it in physics.

Hyperholomorphic connections on coherent sheaves and stability

Misha Verbitsky (2011)

Open Mathematics

Let M be a hyperkähler manifold, and F a reflexive sheaf on M. Assume that F (away from its singularities) admits a connection ▿ with a curvature Θ which is invariant under the standard SU(2)-action on 2-forms. If Θ is square-integrable, such sheaf is called hyperholomorphic. Hyperholomorphic sheaves were studied at great length in [21]. Such sheaves are stable and their singular sets are hyperkähler subvarieties in M. In the present paper, we study sheaves admitting a connection with SU(2)-invariant...

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