有限维实单Balinsky-Novikov超代数的分类

夏利猛; 赵珊珊

doi:10.3969/j.issn.1000-5641.201911018

有限维实单Balinsky-Novikov超代数的分类

doi: 10.3969/j.issn.1000-5641.201911018

江苏大学理学院, 江苏镇江　212013

基金项目: 国家自然科学基金(11871249, 11771142); 江苏省自然科学基金(BK20171294)

详细信息

作者简介:
夏利猛, 男, 教授, 研究方向为李代数. E-mail: xialimeng@ujs.edu.cn

中图分类号: O153.3
计量
- 文章访问数: 133
- HTML全文浏览量: 70
- PDF下载量: 4
- 被引次数: 0
出版历程
- 收稿日期: 2019-04-06
- 网络出版日期: 2020-07-20
- 刊出日期: 2020-07-20

Classification of finite-dimensional real simple Balinsky-Novikov superalgebras

Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu　212013, China

摘要

摘要: 有限维Balinsky-Novikov超代数可以看作是Novikov代数的一类超模拟, 其仿射化给出了一类重要的无限维李超代数. 本文主要叙述了它们的一些性质, 并给出了实数域上有限维单Balinsky-Novikov超代数的完全分类.
- Balinsky-Novikov超代数 /
- Novikov代数 /
- 幂零 /
- 分类
Abstract: In this paper, we study finite-dimensional Balinsky-Novikov superalgebras, which can be regarded as a class of superanalogues of Novikov algebras. We describe some of their properties and give the complete classification of finite-dimensional simple Balinsky-Novikov superalgebras over the field of real numbers.
- Balinsky-Novikov superalgebra /
- Novikov algebra /
- nilpotent /
- classification

HTML全文

参考文献(21)

[1]	GELEAND I, DORFMAN I. Hamiltonian operators and algebraic structures related to them [J]. Func Anal Appl, 1979, 13: 13-30.
[2]	BALINSKY A, NOVIKOV S. Poisson brackets of hydrodynamic type, Frobenius algebras and Lie [J]. Soviet Math Dokl, 1985, 32: 228-231.
[3]	OSBORN J. Novikov algebras [J]. Nova J Algebra, 1992(1): 1-14.
[4]	BURDE D. Left symmetric algebras, or pre-Lie algebras in geometry and physics [J]. Cent Eur J Math, 2006(4): 323-357.
[5]	ZELMANOV E. On a class of local translation invariant Lie algebras [J]. Soviet Math Dokl, 1987, 35: 216-218.
[6]	OSBORN J. Simple Novikov algebras with an idempotent [J]. Comm Algebra, 1992, 20: 2729-2753. DOI: 10.1080/00927879208824486.
[7]	XU X P. On simple Novikov algebras and their irreducible modules [J]. J Algebra, 1996, 185(3): 905-934. DOI: 10.1006/jabr.1996.0356.
[8]	GUEDIRI M. On a remarkable class of left-symmetric algebras and its relationship with the class of Novikov algebras [J]. Comm Algebra, 2016, 44: 2919-2937. DOI: 10.1080/00927872.2015.1065853.
[9]	BAI C M, MEND D J. The classification of Novikov algebras in low dimensions: Invariant bilinear forms [J]. J Phys A, 2001, 34(39): 8193-8197. DOI: 10.1088/0305-4470/34/39/401.
[10]	BENES T, BURDE D. Classification of orbit closures in the variety of 3-dimmensional Novikov algebras [J]. J Algebra Appl, 2014, 13(2): 1350081. DOI: 10.1142/S0219498813500813.
[11]	DZHUMADIL’DAVE A, ZUSMANOVICH P. Commutative 2-cocycles on Lie algebras [J]. J Algebra, 2010, 324: 732-748. DOI: 10.1016/j.jalgebra.2010.04.030.
[12]	STRACHAN I, SZABLIKOWSKI B. Novikov algebras and a classification of multicomponent Camassa-Holm equations [J]. Stud Appl Math, 2014, 133: 117.
[13]	PEI Y F, BAI C M. Realizations of conformal current-type Lie algebra [J]. J Math Phys, 2010, 51(2): 052302.
[14]	PEI Y F, BAI C M. Novikov algebras and Schrödinger-Virasora Lie algebra [J]. J Phys A, 2011, 44(4): 045201. DOI: 10.1088/1751-8113/44/4/045201.
[15]	ZUSMANOVICH P. A Compendium of Lie structures on tensor products [J]. J Math Sci, 2014, 199(3): 266-288. DOI: 10.1007/s10958-014-1855-6.
[16]	BALINSKY A. Classification of the virasoro, the Neveu-Schwarz, and the Ramond-type simple Lie superalgebras [J]. Functional Anal Appl, 1987, 21: 308-309.
[17]	XU X P. Variational calculus of supervariables and related algebraic structures [J]. J Algebra, 2000, 223(2): 396-437. DOI: 10.1006/jabr.1999.8064.
[18]	AYADI I, BENAYADI S. Symmetric Novikov superalgebras [J]. J Math Physics, 2010, 51: 023501. DOI: 10.1063/1.3269596.
[19]	CHEN Z Q, DING M. A class of Novikov superalgebra [J]. J Lie Theory, 2016, 26: 227-234.
[20]	LIU D, PEI Y F, XIA L M. On finite dimensional simple Novikov superalgebra[J]. Comm Algebra, 2019, 47: 999-1004.
[21]	WANG Y, CHEN Z Q, BAI C M. Classification of Balinsky-Novikov superalgebras with dimension 2\|2 [J]. J Phys A, 2012, 45(22): 225201. DOI: 10.1088/1751-8113/45/22/225201.