Deformation quantization of Leibniz algebras

被引：18
|
作者：
Dherin, Benoit [1 ]
Wagemann, Friedrich [2 ]
机构：
[1] Univ Calif Berkeley, Berkeley, CA 94720 USA
[2] Univ Nantes, F-44035 Nantes, France
来源：
ADVANCES IN MATHEMATICS | 2015年 / 270卷
关键词：
Leibniz algebra; Integration; BCH-formula; Deformation quantization; Non-skew-symmetric Poisson manifolds; POISSON; BRACKETS;
D O I：
10.1016/j.aim.2014.10.022
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we use the local integration of a Leibniz algebra l) using a Baker-Campbell-Hausdorff type formula in order to deformation quantize its linear dual h*. More precisely, we define a natural rack product on the set of exponential functions on h* which extends to a rack action on C-infinity (h*). (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：21 / 48
页数：28
相关论文
共 50 条
  • [21] Representations of Leibniz Algebras
    A. Fialowski
    É. Zs. Mihálka
    [J]. Algebras and Representation Theory, 2015, 18 : 477 - 490
  • [22] Thin Leibniz algebras
    Omirov, B. A.
    [J]. MATHEMATICAL NOTES, 2006, 80 (1-2) : 244 - 253
  • [23] Thin Leibniz algebras
    B. A. Omirov
    [J]. Mathematical Notes, 2006, 80 : 244 - 253
  • [24] Leibniz algebras with derivations
    Apurba Das
    [J]. Journal of Homotopy and Related Structures, 2021, 16 : 245 - 274
  • [25] On the commutator in Leibniz algebras
    Dzhumadil'daev, A. S.
    Ismailov, N. A.
    Sartayev, B. K.
    [J]. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2022, 32 (04) : 785 - 805
  • [26] Representations of Leibniz Algebras
    Fialowski, A.
    Mihalka, E. Zs.
    [J]. ALGEBRAS AND REPRESENTATION THEORY, 2015, 18 (02) : 477 - 490
  • [27] On the toroidal Leibniz algebras
    Liu, Dong
    Lin, Lei
    [J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2008, 24 (02) : 227 - 240
  • [28] Cohomology of Leibniz Algebras
    Wagemann F.
    [J]. Jahresbericht der Deutschen Mathematiker-Vereinigung, 2023, 125 (4) : 239 - 264
  • [29] On the anticommutativity in Leibniz algebras
    Kurdachenko, Leonid A.
    Semko, Nikolaj N.
    Subbotin, Igor Ya
    [J]. ALGEBRA & DISCRETE MATHEMATICS, 2018, 26 (01): : 97 - 109
  • [30] On split Leibniz algebras
    Calderon Martin, Antonio J.
    Sanchez Delgado, Jose M.
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (06) : 1651 - 1663
12345