Nhóm Phản Chiếu và Độ Cứng của Đại Số Poisson Bậc Hai

Alev, J., Farkas, D.R.: Finite group actions on poisson algebras. In: The Orbit Method in Geometry and Physics (Marseille, 2000), Progr. Math, vol. 213, pp 9–28. Birkhäuser, Boston (2003) Alev, J., Polo, P.: A rigidity theorem for finite group actions on enveloping algebras of semisimple Lie algebras. Adv. Math. 111(2), 208–226 (1995) Belov-Kanel, A., Kontsevich, M.: Automorphisms of the Weyl algebra. Lett. Math. Phys. 74(2), 181–199 (2005). https://doi.org/10.1007/s11005-005-0027-5 Benson, D.J.: Polynomial Invariants of Finite Groups London Mathematical Society Lecture Note Series, vol. 190. Cambridge University Press, Cambridge (1993). https://doi.org/10.1017/CBO9780511565809 Borel, A.: Essays in the History of Lie Groups and Algebraic Groups History of Mathematics. vol. 21 American Mathematical Society, Providence, RI; London Mathematical Society. Cambridge (2001) Brown, K.A., Gordon, I.: Poisson orders, symplectic reflection algebras and representation theory. J. Reine Angew. Math. 559, 193–216 (2003). https://doi.org/10.1515/crll.2003.048 Brown, K.A., Zhang, J.J.: Unimodular graded Poisson Hopf algebras. Bull. Lond. Math. Soc. 50(5), 887–898 (2018). https://doi.org/10.1112/blms.12194 Chevalley, C.: Invariants of finite groups generated by reflections. Amer. J. Math. 77, 778–782 (1955) Dixmier, J.: Sur les algèbres de Weyl. Bull. Soc. Math. France 96, 209–242 (1968) Ferraro, L., Moore, W.F.: Differential graded algebra over quotients of skew polynomial rings by normal elements. Trans. Amer. Math. Soc. 373(11), 7755–7784 (2020). https://doi.org/10.1090/tran/8132 Gaddis, J.: The isomorphism problem for quantum affine spaces, homogenized quantized Weyl algebras, and quantum matrix algebras. J. Pure Appl. Algebra 221(10), 2511–2524 (2017). https://doi.org/10.1016/j.jpaa.2016.12.036 Gaddis, J., Wang, X.: The Zariski cancellation problem for Poisson algebras. J. Lond. Math. Soc. (2) 101(3), 1250–1279 (2019) Goodearl, K.R.: Semiclassical limits of quantized coordinate rings. In: Advances in ring theory, Trends Math. https://doi.org/10.1007/978-3-0346-0286-0∖_12, pp 165–204. Birkhäuser/Springer, Basel (2010) Kirkman, E., Kuzmanovich, J., Zhang, J.J.: Rigidity of graded regular algebras. Trans. Amer. Math. Soc. 360(12), 6331–6369 (2008). https://doi.org/10.1090/S0002-9947-08-04571-6 Kirkman, E., Kuzmanovich, J., Zhang, J.J.: Shephard-Todd-Chevalley theorem for skew polynomial rings. Algebr. Represent. Theory 13(2), 127–158 (2010). https://doi.org/10.1007/s10468-008-9109-2 Kirkman, E., Kuzmanovich, J., Zhang, J.J.: Invariant theory of finite group actions on down-up algebras. Transform. Groups 20(1), 113–165 (2015). https://doi.org/10.1007/s00031-014-9279-4 Launois, S., Topley, L.: The orbit method for Poisson orders. Proc. Lond. Math. Soc. (3) 120(1), 65–94 (2020). https://doi.org/10.1112/plms.12287 Laurent-Gengoux, C., Pichereau, A., Vanhaecke, P.: Poisson Structures Grundlehren Der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 347. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-31090-4 Lü, J., Wang, X., Zhuang, G.: Universal enveloping algebras of Poisson Ore extensions. Proc. Amer. Math. Soc. 143(11), 4633–4645 (2015). https://doi.org/10.1090/S0002-9939-2015-12631-7 Lü, J., Wang, X., Zhuang, G.: Homological unimodularity and calabi-Yau condition for Poisson algebras. Lett. Math. Phys. 107(9), 1715–1740 (2017). https://doi.org/10.1007/s11005-017-0967-6 Luo, J., Wang, S.Q., Wu, Q.S.: Twisted poincaré duality between Poisson homology and Poisson cohomology. J. Algebra 442, 484–505 (2015). https://doi.org/10.1016/j.jalgebra.2014.08.023 Neusel, M.D., Smith, L.: Invariant Theory of Finite Groups Mathematical Surveys and Monographs, vol. 94. American Mathematical Society, Providence, RI (2002). https://doi.org/10.1086/342122 Oh, S.Q.: Poisson enveloping algebras. Comm. Algebra 27(5), 2181–2186 (1999). https://doi.org/10.1080/00927879908826556 Oh, S.Q.: Poisson polynomial rings. Comm. Algebra 34(4), 1265–1277 (2006). https://doi.org/10.1080/00927870500454463 Polishchuk, A.: Algebraic geometry of Poisson brackets. J. Math. Sci. (New York) 84(5), 1413–1444 (1997). https://doi.org/10.1007/BF02399197. Algebraic geometry, 7 Przybysz, R.: On one class of exact Poisson structures. J. Math. Phys. 42(4), 1913–1920 (2001). https://doi.org/10.1063/1.1346588 Serre, J.P.: Groupes Finis D’automorphismes D’anneaux Locaux Réguliers. In: Colloque D’Algèbre (Paris, 1967), Exp. 8, p 11. Secrétariat mathématique, Paris (1968) Shephard, G.C., Todd, J.A.: Finite unitary reflection groups. Canadian J. Math. 6, 274–304 (1954) Smith, S.P.: Can the Weyl algebra be a fixed ring. Proc. Amer. Math. Soc. 107(3), 587–589 (1989) Tikaradze, A.: The Weyl algebra as a fixed ring. Adv. Math. 345, 756–766 (2019). https://doi.org/10.1016/j.aim.2019.01.005 Tikaradze, A.: Derived invariants of the fixed ring of enveloping algebras of semisimple Lie algebras. Math. Z. 297(1-2), 475–481 (2021) Umirbaev, U.: Universal enveloping algebras and universal derivations of Poisson algebras. J. Algebra 354, 77–94 (2012). https://doi.org/10.1016/j.jalgebra.2012.01.003 Vancliff, M.: The defining relations of quantum n × n matrices. J. London Math. Soc. (2) 52 (2), 255–262 (1995). https://doi.org/10.1112/jlms/52.2.255 Walton, C., Wang, X., Yakimov, M.: Poisson geometry and representations of PI 4-dimensional Sklyanin algebras. 1–52. arXiv:1802.06487 (2018) Walton, C., Wang, X., Yakimov, M.: Poisson geometry of PI three-dimensional Sklyanin algebras. Proc. Lond. Math. Soc. (3) 118(6), 1471–1500 (2019). https://doi.org/10.1112/plms.12220 Watanabe, K.: Certain invariant subrings are Gorenstein. I, II. Osaka. Math. J. 11, 1–8; ibid 11(1974), 379–388 (1974) Xu, P.: Gerstenhaber algebras and BV-algebras in Poisson geometry. Comm. Math. Phys. 3(200), 545–560 (1999)