Universal Enveloping Algebras of Poisson Superalgebras

被引：0
作者：
Lamkin, Thomas [1 ,2 ]
机构：
[1] Miami Univ, Dept Math, 301 S Patterson Ave, Oxford, OH 45056 USA
[2] UCSD, Dept Math Current, 9500 Gilman Dr, La Jolla, CA 92093 USA
来源：
ALGEBRAS AND REPRESENTATION THEORY | 2025年 / 28卷 / 01期
关键词：
Poisson superalgebra; Enveloping algebra; Lie-Rinehart superalgebra; PBW Theorem; COHOMOLOGY;
D O I：
10.1007/s10468-024-10312-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we define and study the universal enveloping algebra of a Poisson superalgebra. In particular, a new PBW Theorem for Lie-Rinehart superalgebras is proved leading to a PBW Theorem for Poisson superalgebras, we show the universal enveloping algebra of a Poisson Hopf superalgebra (resp. Poisson-Ore extension) is a Hopf superalgebra (resp. iterated Ore extension), and we study the universal enveloping algebra for interesting classes of Poisson superalgebras such as Poisson symplectic superalgebras.
引用
收藏
页码：157 / 191
页数：35
相关论文
共 30 条
  • [1] Aissaoui S., 2014, SIGMA. Symmetry, Integrability and Geometry: Methods and Applications, P10
  • [2] Unimodular graded Poisson Hopf algebras
    Brown, Kenneth A.
    Zhang, James J.
    [J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2018, 50 (05) : 887 - 898
  • [3] Bimodules and branes in deformation quantization
    Calaque, Damien
    Felder, Giovanni
    Ferrario, Andrea
    Rossi, Carlo A.
    [J]. COMPOSITIO MATHEMATICA, 2011, 147 (01) : 105 - 160
  • [4] Carmeli C, 2011, EMS SER LECT MATH, P1, DOI 10.4171/097
  • [5] DRINFELD VG, 1985, DOKL AKAD NAUK SSSR+, V283, P1060
  • [6] Smoothness of algebraic supervarieties and supergroups
    Fioresi, Rita
    [J]. PACIFIC JOURNAL OF MATHEMATICS, 2008, 234 (02) : 295 - 310
  • [7] CLIFFORD AND WEYL SUPERALGEBRAS AND SPINOR REPRESENTATIONS
    HARTWIG, J. O. N. A. S. T.
    SERGANOVA, V. E. R. A.
    [J]. TRANSFORMATION GROUPS, 2020, 25 (04) : 1185 - 1207
  • [8] HUEBSCHMANN J, 1990, J REINE ANGEW MATH, V408, P57
  • [9] Korogodski L. I., 1998, Algebras of Functions on QuantumGgroups. Part I
  • [10] Poisson enveloping algebras and the Poincare-Birkhoff-Witt theorem
    Lambre, Thierry
    Ospel, Cyrille
    Vanhaecke, Pol
    [J]. JOURNAL OF ALGEBRA, 2017, 485 : 166 - 198
123