Cohomological comparison theorem
Copyright policy )Cohomological comparison theorem
If $f$ is an idempotent in a ring $Λ$, then we find sufficient \linebreak conditions which imply that the cohomology rings $\oplus_{n\ge 0}Ext^n_Λ(Λ/{\br},Λ/{\br})$ and \linebreak $\oplus_{n\ge 0}Ext^n_{fΛf}(fΛf/f{\br} f,fΛf/f{\br} f)$ are eventually isomorphic. This result allows us to compare finite generation and GK dimension of the cohomology rings $Λ$ and $fΛf$. We are also able to compare the global dimensions of $Λ$ and $fΛf$.
- University of Nordland Norway
- Universidade de São Paulo Brazil
- UNIVERSIDADE DE SAO PAULO Brazil
- Virginia Tech United States
- Nord University Norway
Primary 16W50, 16E30. Secondary 16G10}, projective dimension, Gelfand-Kirillov, Graded rings and modules (associative rings and algebras), idempotent, cohomology rings, group-graded, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), finite generation, Growth rate, Gelfand-Kirillov dimension, FOS: Mathematics, VDP::Mathematics and natural science: 400::Mathematics: 410::Algebra/algebraic analysis: 414, Representation Theory (math.RT), Mathematics - Representation Theory
Primary 16W50, 16E30. Secondary 16G10}, projective dimension, Gelfand-Kirillov, Graded rings and modules (associative rings and algebras), idempotent, cohomology rings, group-graded, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), finite generation, Growth rate, Gelfand-Kirillov dimension, FOS: Mathematics, VDP::Mathematics and natural science: 400::Mathematics: 410::Algebra/algebraic analysis: 414, Representation Theory (math.RT), Mathematics - Representation Theory
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