-(bi)derivations and transposed Poisson algebra structures on Lie algebras

References

• Filippov VT. On δ-derivations of Lie algebras. Sib Math J. 1998;39:1218–1230.
   Web of Science ®Google Scholar
• Jacobson N. Lie algebras. New York (NY): Interscience Publishers; 1962.
   Google Scholar
• Brown RB, Hopkins NC. Noncommutative matrix Jordan algebras, Cayley–Dickson algebras, and Schafer's theorem. Commun Algebra. 1995;23:373–397.
   Web of Science ®Google Scholar
• Dzhumadil'daev A, Zusmanovich P. Commutative 2-cocycles on Lie algebras. J Algebra. 2010;324:732–748.
   Web of Science ®Google Scholar
• Filippov VT. δ-derivations of prime Lie algebras. Sib Math J. 1999;40:174–184.
   Web of Science ®Google Scholar
• Filippov VT. δ-derivations of prime alternative and Maltsev algebras. Algebra Logic. 2000;39:354–358.
   Google Scholar
• Filippov VT. On Lie algebras satisfying an identity of degree 5. Algebra i Logika. 1995;34:235–242.
   Google Scholar
• Zusmanovich P. On δ-derivations of Lie algebras and superalgebras. J Algebra. 2010;324:3470–3486.
   Web of Science ®Google Scholar
• Kaygorodov IB. δ-derivations of simple finite-dimensional Jordan superalgebras. Algebra Logic. 2007;46:318–329.
   Web of Science ®Google Scholar
• Kaygorodov IB. δ-derivations of classical Lie superalgebras. Sib Math J. 2009;50:434–449.
   Web of Science ®Google Scholar
• Brešar M. Centralizing mapping and derivations in prime rings. J Algebra. 1993;156:385–394.
   Web of Science ®Google Scholar
• Brešar M. On generalized biderivations and related maps. J Algebra. 1995;172:764–786.
   Web of Science ®Google Scholar
• Posner EC. Derivations in prime rings. Proc Am Math Soc. 1957;8:1093–1100.
   Google Scholar
• Brešar M. Commuting maps: a survey. Taiwan J Math. 2004;8:361–397.
   Web of Science ®Google Scholar
• Brešar M, Zhao KM. Biderivations and commuting linear maps on Lie algebras. J Lie Theory. 2018;28:885–900.
   Web of Science ®Google Scholar
• Chen ZX. Biderivations and linear commuting maps on simple generalized Witt algebras over a field. Electron J Linear Algebra. 2016;31:1–12.
   Web of Science ®Google Scholar
• Han X, Wang DY, Xia CG. Linear commuting maps and biderivations on the Lie algebras W(a,b). J Lie Theory. 2016;26:777–786.
   Web of Science ®Google Scholar
• Tang XM. Biderivations, linear commuting maps and commutative post-Lie algebra structures on W-algebras. Commun Algebra. 2017;45:5252–5261.
   Web of Science ®Google Scholar
• Wang DY, Yu XX. Biderivations and linear commuting maps on the Schrödinger–Virasoro Lie algebra. Commun Algebra. 2013;41:2166–2173.
   Web of Science ®Google Scholar
• Li LC. Classical r-matrices and compatible Poisson structures for Lax equations on Poisson algebras. Commun Math Phys. 1999;203:573–592.
   Web of Science ®Google Scholar
• Ginzburg V, Kaledin D. Poisson deformations of symplectic quotient singularities. Adv Math. 2004;186:1–57.
   Web of Science ®Google Scholar
• Van den Bergh M. Double Poisson algebras. Trans Am Math Soc. 2008;360:5711–5769.
   Web of Science ®Google Scholar
• Markl M, Remm E. Algebras with one operation including Poisson and other Lie-admissible algebras. J Algebra. 2006;299:171–189.
   Web of Science ®Google Scholar
• Huebschmann J. Poisson cohomology and quantization. J Reine Angew Math. 1990;408:57–113.
   Web of Science ®Google Scholar
• Kontsevich M. Deformation quantization of Poisson manifolds. Lett Math Phys. 2003;66:157–216.
   Web of Science ®Google Scholar
• Drinfeld V. Quantum groups. In: Proceedings International Congress of Mathematicians; 1986; Berkeley. Providence (RI): American Mathematical Society; 1987. p. 798–820.
   Google Scholar
• Kaygorodov I, Shestakov I, Umirbaev U. Free generic Poisson fields and algebras. Commun Algebra. 2018;46:1799–1812.
   Web of Science ®Google Scholar
• Agore A, Militaru G. Jacobi and Poisson algebras. J Noncomm Geom. 2015;9:1295–1342.
   Web of Science ®Google Scholar
• Cantarini N, Kac V. Classification of linearly compact simple Jordan and generalized Poisson superalgebras. J Algebra. 2007;313:100–124.
   Web of Science ®Google Scholar
• Gerstenhaber M. The cohomology structure of an associative ring. Ann Math. 1963;78:267–288.
   Web of Science ®Google Scholar
• Kosmann-Schwarzbach Y. From Poisson to Gerstenhaber algebras. Ann Inst Fourier. 1996;46:1243–1274.
   Web of Science ®Google Scholar
• Xu XP. Novikov-Poisson algebras. J Algebra. 1997;190:253–279.
   Web of Science ®Google Scholar
• Yao Y, Ye Y, Zhang P. Quiver Poisson algebras. J Algebra. 2007;312:570–589.
   Web of Science ®Google Scholar
• Balinskii AA, Novikov SP. Poisson brackets of hydrodynamic type, Frobenius algebras and Lie algebras. Sov Math Dokl. 1985;32:228–231.
   Google Scholar
• Bai CM, Bai RB, Guo L, et al. Transposed Poisson algebras, Novikov–Posion algebras and 3-Lie algebras. arXiv:2005.01110v1.
   Google Scholar
• Kaygorodov I, Khrypchenko M. Poisson structures on finitary incidence algebras. J Algebra. 2021;578:402–420.
   Web of Science ®Google Scholar
• Ferreira BLM, Kaygorodov I, Lopatkin V. 12-derivations of Lie algebras and transposed Poisson algebras. Rev Real Acad Cienc Exactas, Fís Nat A: Mat. 2021;115:142.
   Web of Science ®Google Scholar
• Hartwig JT, Larsson D, Silvestrov SD. Deformations of Lie algebras using σ-derivation. J Algebra. 2006;295:314–361.
   Web of Science ®Google Scholar
• Henkel M. Schrödinger invariance and strongly anisotropic critical systems. J Stat Phys. 1994;75:1023–1061.
   Web of Science ®Google Scholar
• Unterberger J, Roger C. The Schrödinger–Virasoro algebra. New York (NY): Springer-Verlag Berlin Heidelberg; 2012.
   Google Scholar
• Roger C, Unterberger J. The Schrödinger–Virasoro Lie group and algebra: representation theory and cohomological study. Ann Henri Poincaré. 2006;7:1477–1529.
   Web of Science ®Google Scholar
• Unterberger J. On vertex algebra representations of the Schrödinger–Virasoro algebra. Nucl Phys B. 2009;823:320–371.
   Web of Science ®Google Scholar