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First non-abelian cohomology of topological groups II | ||
| Journal of Algebra and Related Topics | ||
| مقاله 5، دوره 2، شماره 2، اسفند 2014، صفحه 43-61 اصل مقاله (382.83 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| H. Sahleh* ؛ H. E. Koshkoshi | ||
| University of Guilan | ||
| چکیده | ||
| In this paper we introduce a new definition of the first non-abelian cohomology of topological groups. We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-abelian cohomology of a topological group by the notion of a principle homogeneous space. | ||
| کلیدواژهها | ||
| Non-abelian cohomology of topological groups؛ cocompatible triple؛ partially crossed topological bimodule؛ principle homogeneous space | ||
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