Quasi-derivations of the (extended) Schrödinger--Witt algebras
Abstract
The Schrödinger--Witt algebras are infinite-dimensional Lie algebras of local dynamical symmetries of the free Schrödinger equation; they contain the Witt algebra of conformal transformations of the time line and appear in non-equilibrium statistical physics and in non-relativistic conformal field theory. We describe all quasi-derivations of the original and the twisted Schrödinger--Witt algebras. We prove that every quasi-derivation is the sum of a derivation, a trivial 1/2-derivation, a linear map with values in the center, and a finite linear combination of maps from three new families of quasi-derivations. As corollaries, we describe all δ-derivations, all δ-biderivations and all transposed δ-Poisson structures of the Schrödinger--Witt algebras. Finally, we prove that every quasi-derivation of the (original or twisted) extended Schrödinger--Witt algebra is the sum of an inner derivation and a multiple of the identity map. As a consequence, there are no nontrivial δ-derivations (for δ∉ {1/2,1}), δ-biderivations (for δ≠1), and transposed δ-Poisson structures on these algebras.
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BibTeX
@misc{kaygorodov2026quasiderivations,
title = {{Quasi-derivations of the (extended) Schrödinger--Witt algebras}},
author = {Ivan Kaygorodov and Abror Khudoyberdiyev and Zarina Shermatova},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23382},
eprint = {2610.23382},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23382},
note = {CC0},
}
RIS
TY - UNPB
TI - Quasi-derivations of the (extended) Schrödinger--Witt algebras
AU - Ivan Kaygorodov
AU - Abror Khudoyberdiyev
AU - Zarina Shermatova
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23382
UR - https://arxiv.org/abs/2610.23382
AB - The Schrödinger--Witt algebras are infinite-dimensional Lie algebras of local dynamical symmetries of the free Schrödinger equation; they contain the Witt algebra of conformal transformations of the time line and appear in non-equilibrium statistical physics and in non-relativistic conformal field theory. We describe all quasi-derivations of the original and the twisted Schrödinger--Witt algebras. We prove that every quasi-derivation is the sum of a derivation, a trivial 1/2-derivation, a linear map with values in the center, and a finite linear combination of maps from three new families of quasi-derivations. As corollaries, we describe all δ-derivations, all δ-biderivations and all transposed δ-Poisson structures of the Schrödinger--Witt algebras. Finally, we prove that every quasi-derivation of the (original or twisted) extended Schrödinger--Witt algebra is the sum of an inner derivation and a multiple of the identity map. As a consequence, there are no nontrivial δ-derivations (for δ∉ {1/2,1}), δ-biderivations (for δ≠1), and transposed δ-Poisson structures on these algebras.
ER -