Computing the $K$-homology $K$-theory product in splitexact algebraic $KK$-theory
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909723609006080 |
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| author | Burgstaller, Bernhard |
| author_facet | Burgstaller, Bernhard |
| contents | Explicit formulas are indicated that compute the product $z \cdot w$ of a level-one element $z \in KK^G(A,{\bf C})$ and any element $w \in KK^G({\bf C},B)$ in splitexact algebraic $KK^G$-theory, or $KK^G$-theory for $C^*$-algebras, with very special $G$-actions. We also make such products accessible to linear-split half-exact $kk$-theory by verifying the existence of a functor from algebraic splitexact $KK$-theory to $kk$-theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03477 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computing the $K$-homology $K$-theory product in splitexact algebraic $KK$-theory Burgstaller, Bernhard K-Theory and Homology Operator Algebras 19K35, 46L80, 16E20, 20M18 Explicit formulas are indicated that compute the product $z \cdot w$ of a level-one element $z \in KK^G(A,{\bf C})$ and any element $w \in KK^G({\bf C},B)$ in splitexact algebraic $KK^G$-theory, or $KK^G$-theory for $C^*$-algebras, with very special $G$-actions. We also make such products accessible to linear-split half-exact $kk$-theory by verifying the existence of a functor from algebraic splitexact $KK$-theory to $kk$-theory. |
| title | Computing the $K$-homology $K$-theory product in splitexact algebraic $KK$-theory |
| topic | K-Theory and Homology Operator Algebras 19K35, 46L80, 16E20, 20M18 |
| url | https://arxiv.org/abs/2508.03477 |