XXXII Workshop on Geometric Methods in Physics | 30.06-6.07.2013 |

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## Satish Kumar Dixit## STUDIES ON DEFORMATION THEORY OF ALGEBRAIC STRUCTURESThe aim of this paper is to develop a deformation theory which classifies infinitesimal deformations of multi-categories. In order to achieve this, methods from homological algebra will be used: a cochain complex will be constructed such that infinitesimal deformations up to equivalence correspond to elements of the second cohomology group. The thesis starts with presenting the classical result of deformations of associative algebras. On the way we also encounter deformations of Lie algebras and of categories. Gerstenhaber describes in a method to construct a cochain complex bringing us into the arena of homological algebra. The idea of homological algebra is to assign to an object a cochain complex, i.e. a sequence of modules such that the composition of any two consecutive maps is zero. |

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