Borel subalgebras of Lie algebras of vector fields
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909042666897408 |
|---|---|
| author | Arzhantsev, Ivan Zaidenberg, Mikhail |
| author_facet | Arzhantsev, Ivan Zaidenberg, Mikhail |
| contents | In [I. Arzhantsev and M. Zaidenberg, Borel subgroups of the automorphism groups of affine toric surfaces, arXiv:2507.09679 (2025)] we described the Borel subgroups and maximal solvable subgroups of the automorphism groups of affine toric surfaces. In the present paper, we introduce the notion of an integrable Borel subalgebra in the Lie algebra of the automorphism group of an affine variety. We show that they are precisely the tangent algebras of the Borel subgroups. We classify the integrable Borel subalgebras in the Lie algebras of the automorphism groups of toric affine surfaces, notably of the affine plane and its cyclic quotients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17223 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Borel subalgebras of Lie algebras of vector fields Arzhantsev, Ivan Zaidenberg, Mikhail Algebraic Geometry Primary 14J50, 17B66, Secondary 14R10, 17B45, 22E65 In [I. Arzhantsev and M. Zaidenberg, Borel subgroups of the automorphism groups of affine toric surfaces, arXiv:2507.09679 (2025)] we described the Borel subgroups and maximal solvable subgroups of the automorphism groups of affine toric surfaces. In the present paper, we introduce the notion of an integrable Borel subalgebra in the Lie algebra of the automorphism group of an affine variety. We show that they are precisely the tangent algebras of the Borel subgroups. We classify the integrable Borel subalgebras in the Lie algebras of the automorphism groups of toric affine surfaces, notably of the affine plane and its cyclic quotients. |
| title | Borel subalgebras of Lie algebras of vector fields |
| topic | Algebraic Geometry Primary 14J50, 17B66, Secondary 14R10, 17B45, 22E65 |
| url | https://arxiv.org/abs/2510.17223 |