Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.20012 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909233204690944 |
|---|---|
| author | Hartwig, Jonas T. |
| author_facet | Hartwig, Jonas T. |
| contents | Galois orders, introduced by Futorny and Ovsienko, is a class of noncommutative algebras that includes generalized Weyl algebras, the enveloping algebra of the general linear Lie algebra and many others. We prove that the noncommutative Kleinian singularities of type $D$ can be realized as principal Galois orders. Our starting point is an embedding theorem due to Boddington. We also compute explicit generators for the corresponding (Morita equivalent) flag order, as a subalgebra of the nil-Hecke algebra of type $A_1^{(1)}$. Lastly, we compute structure constants for Harish-Chandra modules of local distributions and give a visual description of their structure from which subquotients are easily obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_20012 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Galois order realization of noncommutative type $D$ Kleinian singularities Hartwig, Jonas T. Representation Theory Galois orders, introduced by Futorny and Ovsienko, is a class of noncommutative algebras that includes generalized Weyl algebras, the enveloping algebra of the general linear Lie algebra and many others. We prove that the noncommutative Kleinian singularities of type $D$ can be realized as principal Galois orders. Our starting point is an embedding theorem due to Boddington. We also compute explicit generators for the corresponding (Morita equivalent) flag order, as a subalgebra of the nil-Hecke algebra of type $A_1^{(1)}$. Lastly, we compute structure constants for Harish-Chandra modules of local distributions and give a visual description of their structure from which subquotients are easily obtained. |
| title | Galois order realization of noncommutative type $D$ Kleinian singularities |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2406.20012 |