PreprintCC BY-NC 4.0HAL
Borel subalgebras of Lie algebras of vector fields
Abstract
Let X be an affine variety. In the present paper, we introduce the notion of a locally integrable Borel subalgebra of the Lie algebra Lie(Aut(X)). We show that these are precisely the tangent algebras of the Borel subgroups of Aut(X). We classify the locally integrable Borel subalgebras in the Lie algebras of the groups Aut(S) of toric affine surfaces S, notably of the affine plane and its cyclic quotients. See [5] for a description of the Borel subgroups and, more generally, maximal solvable subgroups of Aut(S).
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BibTeX
@misc{zaidenberg2026borel,
title = {{Borel subalgebras of Lie algebras of vector fields}},
author = {M Zaidenberg and Ivan Arzhantsev},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05843291v1},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - Borel subalgebras of Lie algebras of vector fields
AU - M Zaidenberg
AU - Ivan Arzhantsev
PY - 2026
DA - 2026/10/29
PB - HAL
UR - https://hal.science/hal-05843291v1
AB - Let X be an affine variety. In the present paper, we introduce the notion of a locally integrable Borel subalgebra of the Lie algebra Lie(Aut(X)). We show that these are precisely the tangent algebras of the Borel subgroups of Aut(X). We classify the locally integrable Borel subalgebras in the Lie algebras of the groups Aut(S) of toric affine surfaces S, notably of the affine plane and its cyclic quotients. See [5] for a description of the Borel subgroups and, more generally, maximal solvable subgroups of Aut(S).
ER -