In the thesis we introduce and study cohomology theories of <i>A</i><sub>∞</sub>-algebras. There are two theories: Hochschild cohomology and Shukla cohomology. Hochschild cohomology classifies split extensions of <i>A</i><sub>∞</sub>-algebras, while Shukla cohomology is introduced to classify all extensions. Standard theorems are generalized for introduced cohomology theories. Thanks to the properties of <i>A</i><sub>∞</sub>-algebras mentioned theorems are formulated in much more general form rather than for standard cases. This generality implies nontrivial results if we substitute instead of <i>A</i><sub>∞</sub>-algebras an associative algebra.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:430410 |
| Date | January 2006 |
| Creators | Kurdiani, R. |
| Publisher | University of Aberdeen |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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