Koszul pairs and applications
| Autor: | Javier López Peña, Pascual Jara, Dragoş Ştefan |
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| Rok vydání: | 2010 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Mathematics::Commutative Algebra 010102 general mathematics Mathematics::Rings and Algebras K-Theory and Homology (math.KT) Mathematics - Rings and Algebras 01 natural sciences Mathematics::Algebraic Topology Mathematics::K-Theory and Homology Rings and Algebras (math.RA) 0103 physical sciences Mathematics - K-Theory and Homology FOS: Mathematics 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematical Physics Mathematics |
| DOI: | 10.48550/arxiv.1011.4243 |
| Popis: | Let $R$ be a semisimple ring. A pair $(A,C)$ is called almost-Koszul if $A$ is a connected graded $R$-ring and $C$ is a compatible connected graded $R$-coring. To an almost-Koszul pair one associates three chain complexes and three cochain complexes such that one of them is exact if and only if the others are so. In this situation $(A,C)$ is said to be Koszul. One proves that a connected $R$-ring $A$ is Koszul if and only if there is a connected $R$-coring $C$ such that $(A,C)$ is Koszul. This result allows us to investigate the Hochschild (co)homology of Koszul rings. We apply our method to show that the twisted tensor product of two Koszul rings is Koszul. More examples and applications of Koszul pairs, including a generalization of Fr\"oberg Theorem, are discussed in the last part of the paper. Comment: The final version, accepted for publication in Journal of Noncommutative Geometry |
| Databáze: | OpenAIRE |
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