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Finite-Dimensional 2-Generated Lie Algebras of Derivations on T-Varieties

Siberian Mathematical Journal. 2025. Vol. 66. No. 3. P. 715–727.
D. A. Matveev

We consider an affine algebraic variety with a torus action of complexity one. It is known
that in this case homogeneous locally nilpotent derivations on the algebra of functions of this variety
are defined in terms of a polyhedral divisor. In the present paper, a formula is obtained for multiple
commutators of two homogeneous locally nilpotent derivations with at most one derivation of horizontal
type. Using the obtained formula, a criterion is derived for finite dimensionality of Lie algebras generated
by a pair of homogeneous locally nilpotent derivations in the Lie algebra of all derivations of the algebra
of functions on a variety with a torus action.

Research target: Mathematics
Language: English
Full text
DOI
Keywords: Lie algebraалгебра Лиlocally nilpotent derivationлокально нильпотентное дифференцированиеGraded algebraградуированная алгебраT-varietyT-многообразиеcommutator of derivationsкоммутатор дифференцирований
Publication based on the results of:
Automorphism groups of algebraic varieties (2025)
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