The Universal Enveloping Algebra of the Schrodinger Algebra and its Prime Spectrum

被引：15

作者：

Bavula, V. V. ^{[1
]}

Lu, T. ^{[2
]}

机构：

[1] Univ Sheffield, Dept Pure Math, Hicks Bldg, Sheffield S3 7RH, S Yorkshire, England

[2] Huaqiao Univ, Sch Math Sci, Quanzhou 362021, Fujian, Peoples R China

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2018年 / 61卷 / 04期

关键词：

prime ideal; weight module; simple module; centralizer; Whittaker module; SIMPLE WEIGHT MODULES; CLASSIFICATION; REPRESENTATIONS; FINITE;

D O I：

10.4153/CMB-2018-009-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The prime, completely prime, maximal, and primitive spectra are classified for the universal enveloping algebra of the Schrodinger algebra. The explicit generators are given for all of these ideals. A counterexample is constructed to the conjecture of Cheng and Zhang about non-existence of simple singular Whittaker modules for the Schrodinger algebra (and all such modules are classified). It is proved that the conjecture holds 'generically'.

引用

页码：688 / 703

页数：16

共 18 条

[1] Intertwining operator realization of non-relativistic holography [J].

Aizawa, N. ;

Dobrev, V. K. .

NUCLEAR PHYSICS B, 2010, 828 (03) :581-593

[2] The simple modules of the ore extensions with coefficients from a Dedekind ring [J].

Bavula, V .

COMMUNICATIONS IN ALGEBRA, 1999, 27 (06) :2665-2699

[3]

Bavula VV, 2018, J LIE THEORY, V28, P525

[4] Classification of Simple Weight Modules over the Schrodinger Algebra [J].

Bavula, V. V. ;

Lu, T. .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2018, 61 (01) :16-39

[5] The Prime Spectrum and Simple Modules Over the Quantum Spatial Ageing Algebra [J].

Bavula, V. V. ;

Lu, T. .

ALGEBRAS AND REPRESENTATION THEORY, 2016, 19 (05) :1109-1133

[6]

Bavula V. V., 1993, UKR MATH J, V45, P329, DOI DOI 10.1007/BF01061007

[7]

Bavula V.V., 1993, Ukrain. Mat. Zh, V45, P223, DOI DOI 10.1007/BF01060977

[8] THE IRREDUCIBLE REPRESENTATIONS OF THE LIE-ALGEBRA SL(2) AND OF THE WEYL ALGEBRA [J].

BLOCK, RE .

ADVANCES IN MATHEMATICS, 1981, 39 (01) :69-110

[9] Quasi-Whittaker modules for the Schrodinger algebra [J].

Cai, Yan-an ;

Cheng, Yongsheng ;

Shen, Ran .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 463 :16-32

[10]

Dixmier J., 1996, GRADUATE STUDIES MAT, V11, DOI DOI 10.1090/GSM/011

← 1 2 →