Higher structures on homology groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910481038442496 |
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| author | Kowalzig, Niels Pratali, Francesca |
| author_facet | Kowalzig, Niels Pratali, Francesca |
| contents | We dualise the classical fact that an operad with multiplication leads to cohomology groups which form a Gerstenhaber algebra to the context of cooperads: as a result, a cooperad with comultiplication induces a homology theory that is endowed with the structure of a Gerstenhaber coalgebra, that is, it comes with a graded cocommutative coproduct which is compatible with a coantisymmetric cobracket in a dual Leibniz sense. As an application, one obtains Gerstenhaber coalgebra structures on Tor groups over bialgebras or Hopf algebras, as well as on Hochschild homology for Frobenius algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06710 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher structures on homology groups Kowalzig, Niels Pratali, Francesca Algebraic Topology K-Theory and Homology Quantum Algebra We dualise the classical fact that an operad with multiplication leads to cohomology groups which form a Gerstenhaber algebra to the context of cooperads: as a result, a cooperad with comultiplication induces a homology theory that is endowed with the structure of a Gerstenhaber coalgebra, that is, it comes with a graded cocommutative coproduct which is compatible with a coantisymmetric cobracket in a dual Leibniz sense. As an application, one obtains Gerstenhaber coalgebra structures on Tor groups over bialgebras or Hopf algebras, as well as on Hochschild homology for Frobenius algebras. |
| title | Higher structures on homology groups |
| topic | Algebraic Topology K-Theory and Homology Quantum Algebra |
| url | https://arxiv.org/abs/2406.06710 |