The Adjoint Representation of a Higher Lie Groupoid
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911828756398080 |
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| author | Trentinaglia, Giorgio |
| author_facet | Trentinaglia, Giorgio |
| contents | We extend the standard construction of the adjoint representation of a Lie groupoid to the case of an arbitrary higher Lie groupoid. As for a Lie groupoid, the adjoint representation of a higher Lie groupoid turns out to be a representation up to homotopy which is well defined up to isomorphism. Its existence and uniqueness are immediate consequences of a more general result in the theory of simplicial vector bundles: the representation up to homotopy obtained by splitting a higher vector bundle by means of a cleavage is, to within isomorphism, independent of the choice of the cleavage. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14908 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Adjoint Representation of a Higher Lie Groupoid Trentinaglia, Giorgio Category Theory Differential Geometry Primary 18N25, 18N50, Secondary 18G31, 18G35 We extend the standard construction of the adjoint representation of a Lie groupoid to the case of an arbitrary higher Lie groupoid. As for a Lie groupoid, the adjoint representation of a higher Lie groupoid turns out to be a representation up to homotopy which is well defined up to isomorphism. Its existence and uniqueness are immediate consequences of a more general result in the theory of simplicial vector bundles: the representation up to homotopy obtained by splitting a higher vector bundle by means of a cleavage is, to within isomorphism, independent of the choice of the cleavage. |
| title | The Adjoint Representation of a Higher Lie Groupoid |
| topic | Category Theory Differential Geometry Primary 18N25, 18N50, Secondary 18G31, 18G35 |
| url | https://arxiv.org/abs/2312.14908 |